During the long hot summer of '76, few sights in the mugger-haunted subways of New York were as chilling as the faces of Mack the Knife and Hamlet.

Larger than life, Threepenny Opera's sinister hero, Mack, stared out from billboards with cold-blooded eyes, while a demonic Prince of Denmark raged against a blood-red background. Both posters, commissioned by the New York Shakespeare Festival, were the inspiration of Oklahoma-born artist Paul Davis, 40. Like other Davis works, they have become collector's items.

The Threepenny Opera poster now belongs to the Museum of Modern Art, and a Davis painting, Matthew's Cat, was both the museum's 1975 Christmas card and the cover of a 1976 book, The Illustrated Cat. Twenty-nine of the artist's posters and paintings were recently published as an outsize Dutton paperback which is about to go into a second printing. Threepenny Opera alone has sold 50,000 copies in poster shops across the country.

"I never wanted to be anything but a magazine illustrator," Davis says. He began sketching home scenes and sent them to his father, a Methodist minister stationed in Alaska during World War II as an Army chaplain. At 17, encouraged by his Tulsa high school art teacher, Davis won a scholarship to New York's School of Visual Arts. While still a student, he sold a cartoon to Playboy. After graduation in 1959, he joined Push Pin, the hottest commercial art studio in New York, headed by Seymour Chwast and Milton Glaser. "Paul had a unique, personal vision very early," says Glaser. "He was most impressive even then."

Davis' blend of surrealism and sophisticated primitivism won him assignments from Esquire, McCall's and Holiday. "Those were the golden years of big magazine formats and big budgets," recalls Davis. By 1970, however, "the free ride for magazine illustrators was over," he says. "I did more and more ads and got more and more depressed. Luckily, along came Olivetti."

The Italian office machine company hired Davis to paint 12 scenes of Americana for its elegant appointments calendar in 1974. Next Olivetti commissioned an illustrated private edition of Thoreau's Walden. "From then on," he says, "the galleries were interested."

Today he is appreciated worldwide. In 1975 Davis exhibited in several museums in Japan; last year he was the first American artist to show his work at the new Centre Georges Pompidou (called the Beaubourg) in Paris. With a one-man show now in progress in Milan, Davis commands as much as $8,000 a canvas.

Though his reputation as a painter is established, Davis has no intention of giving up posters. "I want my work to appeal to the widest spectrum of people," he says. "An artist who doesn't admit that is kidding himself."

Davis, his second wife, Myrna, 41, a writer, and son Matthew, 10, along with two dogs and two cats, live in an 1860 yellow frame house in the old Long Island seaport town of Sag Harbor. Paul paints in a converted double garage; Myrna writes in a remodeled downstairs bedroom. In 1972 she wrote and edited The Potato Book, a compendium of recipes from local celebrities, with an introduction by neighbor Truman Capote.

On Davis' drawing board are posters for Mike Nichols' new musical, Alice, and for a nine-hour NBC dramatization about the war, Holocaust. He is also working on new paintings for his first New York retrospective, scheduled for next year. Before his career ends, the family menagerie is likely to end up immortalized on canvas. Even the Davises' elusive and grumpy cat, Max, was the cover of Neiman-Marcus' 1977 Christmas catalogue. Explains Davis: "When I can't think of anything else, I just paint one of the animals."