Rarely are relationships between creative individuals and institutions as fertile as the one enjoyed by Andy Goldsworthy and the Yorkshire Sculpture Park (YSP). 'We're probably made for each other, and we probably made each other,' says Goldsworthy, one of Britain's leading land artists whose latest, and biggest ever, show has just opened at the YSP.

The park is celebrating 30 years of business this year, and Goldsworthy, who first made an artwork there back in 1983, and was artist in residence in 1987, is the ideal choice to help it do so.

The artist only works with natural, local materials and prefers his pieces fully integrated in nature, making the YSP's 500 acres of rolling landscaped countryside well suited to his requirements. And there are notable parallels in the evolution of his career with the history of the park.

Both began humbly in the 1970s. Goldsworthy traces his career back to 1976 when he started making ephemeral outdoor pieces such as covering himself in sand, and stacking boulders against the incoming tide. A year later the park opened to the public under the aegis of the still incumbent director Peter Murray with a mere 15 acres to its name, part of what had been the private park of Bretton Hall College, an offshoot of Leeds University.

Goldsworthy has gone on to make artworks all over the world, including tree sculptures in the Arctic, giant walls in America and one-tonne snowballs that were placed, to the surprise of commuters, in the centre of London.

If art critics don't rate him as highly as the main competition, fellow land artist Richard Long (who has a major retrospective at the Scottish National Gallery of Modern Art later this year), the public have embraced him like few others in any field of contemporary art. His series of books of photographs of his work from Thames & Hudson are among the art publisher's most successful publications.

Over the same stretch of time, the park has gone through a series of expansions. Although much of its land is still farmed, the YSP trust now owns about half of the full 500 acres of the original 18th-century Bretton estate where it is sited, and leases the rest.

It has also developed indoor spaces: the large halls of the Longside Gallery at the south of the estate, and the elegant four rooms of the Underground Gallery, which is sited next to the visitors' centre and is the newest addition, having opened in 2005.

Artistically, the park has gone from regional tourist attraction to international player, thanks to Murray's great skill at siting artworks in the landscape and the major shows he has organised on Henry Moore, Magdalena Abakanowicz and Joel Schapiro among others. It now gets about 300,000 visitors a year, including 40,000 schoolchildren.

Goldsworthy has a metaphor for the parallels between his own development and the park's: 'In 1987 when I was at the YSP I picked up a few horse-chestnut stalks and pinned them together with thorns. I liked the shape they made, so I thought I'd try and span two trees in the park that were only 18 inches apart. I found I could do it, and now I'm making a screen of horse-chestnut stalks in the Underground Gallery that spans a whole room. I like the sense that the idea has grown both conceptually and physically, and I think that's a nice parallel with what has happened at the YSP.'

His show, the most extensive and labour intensive the park has put on, is seen as a blueprint for what can be done at a sculpture park when artist and staff fully collaborate. It is also an example of why the YSP, at least at this stage, is ahead of its British competitors such as the Grizedale Forest Park in Cumbria and the Cass Sculpture Foundation in West Sussex.

And it shows the park's working process: a mixture of careful planning, and fortuitous sponsorship slotting into place. With no endowment and a 60/40 split of public and private funding, exhibition plans have to be highly flexible.

Murray explains: 'The way we operate is we've got a list as long as my arm in terms of possibilities. And then it's like a game of chess. We move the shows around according to when and where we can get funding.'

In the case of the Goldsworthy show the sponsorship of American private collector Roger Evans has enabled the realisation of an idea first mooted by Murray years ago and developed in greater detail with the park's curatorial team since then. Goldsworthy has created four elaborate permanent outdoor pieces, transformed the Underground Gallery, and filled one of the halls at Longside with artworks that include an entire window caked in animal dung.

The highlight of the outdoor pieces is Hanging Trees, large sections of trees, fixed horizontally in walled pits behind the estate's ha-ha, that took two months to construct. The Underground Gallery boasts a room caked with clay, straw and human hair and that chestnut-stalk screen, among other work.

Thirty volunteers, nine dry-stone wallers and eight technicians have worked alongside Goldsworthy to put the show in place. The key to the project's success, and every large exhibition at the YSP, is the experience and technical know-how of Alan Mackenzie, the park's site manager. Mackenzie has been at the park for 15 years, over the course of which he has invented new ways of moving sculpture.

His ingenious methods have included the fabrication of rubber friction straps in order to lift a six-metre-long column, and rolling an 11-tonne block of Carrara marble over ice cubes. Such skills are part of the reason why Murray and his team are now invited to curate shows the world over.

Goldsworthy's working process is exceptionally hands-on. Not all artists make their work on site, and although the park has several long-terms loans, including work by Antony Gormley and Barbara Hepworth, only two permanent site-specific works pre-date Goldsworthy's additions. One is Sol LeWitt's largest ever sculpture, the other a so-called 'skyscape' by Texan artist James Turrell.

Turrell operated through an assistant for much of the skyscape's construction last year in the YSP's disused deer shelter, although he had first made the proposal after a visit to the park 13 years ago. Financial support presented itself when the Art Fund paid the £750,000 cost as a millennial gift to the nation - an example not only of the lengthy gestation periods of many of the park's projects, but also of how much their timing is dictated by funding.

Although Murray is the YSP's main driving force and ideas man, he is backed by a three-strong curatorial team. Behind most of the smaller shows and residencies at the park (the YSP uses residency as a fairly flexible term for artists who come and work at the park) is Clare Lilley, the park's director of programmes.

Several projects are taking place at any one time - alongside the Goldsworthy show the YSP is working on an off-site project by Cuban artist Carlos Garaicoa, a Kurdish community project, and outdoor pieces to be devised by the poet Simon Armitage. And it is Lilley who makes sure everything complements each other.

'Andy's an exception because he's using every space,' she says. 'Normally we have layered programming at the park with bigger artists in the larger spaces and younger artists in the smaller galleries. I try to get a balance so that when, say, there are sculptures on plinths in the Underground Gallery, I go for something film- or installation-based in the smaller Bothy Gallery.

And then out of doors I try to have projects that engage people in different ways, such as those Alec Finlay initiated last year, where people wrote poetry that responded to the landscape.'

Poetry is something of a theme at the moment, because of Lilley's own interest in the subject. Plans are still under discussion regarding the nature of Armitage's work, but he is hoping to make texts visible in the landscape: 'We've talked about ice and fire, it's quite elemental,' says Lilley. As usual at the YSP, the final artworks will be a result of lengthy negotiations between park and artist.

Lilley says the advantages of working with living artists, the focus of her work, far outweigh the negatives, not only for herself but the park's 100-strong full and part-time staff. The artists are never less than demanding and she frequently has sleepless nights: 'There's a bit of an eleventh-hour scene that goes on here.' But the work is inspiring. 'Everyone loves it. The site team, the gardeners, the estate workers: people really love being involved in hard demanding projects.'

Goldsworthy also believes the success of his favourite venue is down to its work ethic: 'There are so many so-called sculpture parks that are an easy option to dump a few sculptures in a field and that is so different from what is happening here.'

Serena Davies is a freelance arts journalist