Frank Stella wears his credentials as an architect loosely, without too much concern for the pragmatic applications of his designs. “Good architecture has to be watertight,” he said recently, with mock solemnity. Mr. Stella’s designs, however, tend to be more permeable than habitable. He seems similarly unfazed that his architectural designs, along with almost four decades of painting and sculpture, will be the subject of a major exhibition at the Metropolitan Museum of Art next month. “It was their idea, not mine,” the artist said with a shrug.

“Frank Stella: Painting Into Architecture” and a companion exhibit, “Frank Stella on the Roof,” both open May 1 at the Met. The main exhibit of Mr. Stella’s 14 models for pavilions, chapels, and public gardens will be on view in “Frank Stella: Painting Into Architecture,” as well as about a dozen (the exact number has not yet been decided) paintings, wall reliefs, and sculptures. The show on the museum’s roof will feature Mr. Stella’s large-scale sculptural work in stainless steel and carbon fiber. Together, the exhibits demonstrate the complementary natures of architecture and the fine arts — and the fluidity of Mr. Stella’s art making over the last several decades.

Sitting in the back office of the Paul Kasmin Gallery, where more new sculpture work will go on display May 11, Mr. Stella peered at a photograph of one of the models that will be displayed at the Met. “Chinese Pavilion” is a long lattice-work structure that twists and warps in on itself to carve out separate spaces within its shell. Gesturing toward the open diamond-shaped spaces, Mr. Stella explained, “It has to be shelter, and if you make it an open structure, it can be beautiful and everything, but it doesn’t satisfy as architecture.” Mr. Stella’s architectural models are buildable, even if their form takes precedence over function.

But for him, the line between what is art and what is architecture is less important than the exploratory nature of his work. “It’s a space that you are in,” he said. “Rather than experience it as you would, say, Richard Serra, where you have a dramatic experience, this one you could be in and you could sit down and have a drink in it and continue to have an experience of the space. It’s really a question about creating space in the way that you would create a painting.”

Mr. Stella’s large, black-stripe paintings galvanized the world of abstract painting in 1958. “In my current work, the black paintings never cross my mind,” he said. “Adjoeman,” for example, which will be installed on the Met’s roof, is a colossal sculpture constructed of stainless steel and carbon fiber. The steel appears as malleable as rope as it loops over and around the 3,000-pound structure. Mr. Stella, who turns 71 next month, has traveled far beyond the formal austerity of minimalism that characterized his early, career-making work. The voluptuous curve appears to have all but displaced clean, angled geometry. Mr. Stella said the real question for him is, “Why did have I to tie myself in knots to escape the rectangle?”

What remains from his earliest work, however, is Mr. Stella’s fascination with dynamism and assemblage. If Renaissance artists panegyrized “arte a nasconder l’arte,” art that hides its presence, Mr. Stella turns this precept inside out, exposing to the viewer the mechanics of the work’s creation. “I built the stretchers that I painted the black paintings on,” Mr. Stella said. “So I’ve been building paintings since the beginning. To extend the building of paintings into the building of sculpture, into building habitable structures, it’s really about construction, putting things together.”

Mr. Stella received his first architectural commission in 1991, a design for a public garden in Germany that was ultimately rejected by government authorities. At the time, he was enormously dissatisfied with the creative lack in modern structures. “I was taken with the idea that what was killing architecture was units,” he said. “Identical panes of glass, one floor on top of another. It’s the tyranny of square footage. None of my works have any repeatable units in them. All the geometry moves and twists.” Few of Mr. Stella’s architectural works have been realized, although one, “The Broken Jug,” was built inside a shipyard in Cherbourg, France. Large sections of the model will be part the Met’s exhibit.

Mr. Stella said he thinks that many recent architectural developments in New York City are impressive. “Frank Gehry’s new building is wonderful. All of a sudden, boom, it’s there,” he said. And despite his own near abandonment of the rectangle, Stella also admires the Seagram building and the Lever House. As for the World Trade Center buildings, “I thought they were awful, but now they’re gone, I miss them. And I feel that the only statement that one can make about that kind of thing is to just put it right back up.”

Today, Mr. Stella splits his time between his foundry workshop in Newburgh, N.Y., and what he insists is a perfectly ordinary, watertight home in New York City. His sons and grandchildren often stay there with him. “It is still not an empty nest,” he said, “which I kind of like.”

As for Mr. Stella’s upcoming exhibition, at the Met, he said it’s a bittersweet experience. In 1970, his friend Henry Geldzahler curated the museum’s first exhibition of modern American art. “The Courbets and Manets were taken down and the David Smiths and the Kenneth Nolands and Andy Warhols were shown in that space. It was a shocking experience and a defining moment for modern art,” Mr. Stella said. Geldzahler died of cancer at age 59 in 1994. “For me, the Met is about Henry. He’s my friend and Henry’s gone now. All of the really best part of my life in the art world is with Henry. So this is like coming home to me. It’s like I’m being there with Henry.”

Those issues of loss and legacy, however, haven’t distracted Mr. Stella from the task at hand. Throughout his more than 50 years of prolific art-making, one constant has remained. “From my own point of view,” he said, “it’s just about doing it, which it probably was at every other stage of my life.”