“My furniture, I like to think, is elegance with tranquility,” Mr. Kagan said . (Vittorio Zunino Celotto/Getty Images)

Vladi­mir Kagan, who brought a sensual aesthetic to modern furniture design with kidney-shaped couches among other innovative seating concepts that were credited with rounding off the hard edges of contemporary style, died April 7 at his home in Palm Beach, Fla. He was 88.

The cause was a heart attack, said his daughter Vanessa Kagan Diserio.

A cabinetmaker’s son, Mr. Kagan came to the United States at 11 after fleeing Nazi Germany with his family. He trained at his father’s New York workshop and by the 1940s was producing his own designs. One of his first orders was a set of tables and chairs for a delegate lounge at the fledgling United Nations.

In the decades that followed, he became one of the most sought-after designers of his era, his works housed in the homes of Hollywood celebrities and enshrined in the collections of the Brooklyn Museum, the Cooper Hewitt design museum in New York and other institutions.

“I’m very accessible,’’ he once quipped to the New York Times, “but I’m amongst museum pieces.”

Mr. Kagan advocated “elegance with tranquility” and did not forsake comfort for stylishness. Many of his designs featured soft curves and overstuffed upholstery.

“Unlike Bauhaus furniture, Kagan’s is so comfortable his clients sit in the living room even when there’s no company,” journalist Sarah Booth Conroy, who often wrote about home design, once noted in The Washington Post.

His work, Conroy observed, would not have been out of place “in a setting for Greta Garbo, an Afghan hound curled at her feet.”

Among Mr. Kagan’s most noted designs, dating to the 1970s, was the Omnibus sofa, a multilevel sectional seating arrangement that he described as an “interior landscape.”

“It expresses what I believe happens in the home, which is that you have more than one focus,” he once told the Toronto Star. “You have a window here, you have a fireplace over here, have a television over there — you want to be able to be mobile in the sitting arrangements, so with this kind of free-flowing center seat you can take advantage of all directions.”

A hallmark of his work was the curved line. One of his most recognizable chairs was a chaise that looked remarkably like a tongue. Another piece, with its back and arms formed by two sculpted strands of leather, was named the Fettuccine chair. Another item, designed in Palm Beach, was called the Hurricane chair.

“I was watching the palm trees in the wind,” Mr. Kagan told the Boston Globe. “The palm trees all bent over in one direction with the wind, but they didn’t break. If you look at the shape of that chair, everything is swept in one direction in the wind. It’s funny how your surroundings can inspire design.”

Mr. Kagan operated a factory on Long Island and showrooms across the United States and in Europe. His clients over the years included movie stars such as Marilyn Monroe and Gary Cooper and, in more recent times, Tom Cruise and Angelina Jolie.

He retired in the late 1980s but was enticed back to work when his designs enjoyed a resurgence of popularity. In 2005, a Serpentine sofa he created in 1952 fetched $192,000 at a Christie’s auction, according to the research of Antiques Roadshow.

Vladimir Illi Kagan was born in Worms on the Rhine, Germany, on Aug. 29, 1927. His father, from ­modern-day Belarus, had served in the Russian army in World War I and was taken prisoner in Germany, where he taught woodworking while in captivity and established a home after the armistice.

In 1938, the family came to the United States, “more I think because we were Russian than because we were Jews,” Mr. Kagan told The Post. He attended the High School of Art and Design in New York and studied architecture at Columbia University, and then partnered with Hugo Dreyfuss, a textile designer and printer, to form an interior-design business in New York in the 1950s. Mr. Kagan later continued the operation on his own.

In 1957, he married Erica Wilson, a British-born needlework artist whose books and public-television programs made her known as “America’s first lady of stitchery.” The couple’s home in New York was filled with his designs and her needlework, as well as, for many years, dozens of birds that they housed in an aviary.

Mr. Kagan’s wife died in 2011. Survivors include their three children, Jessica Kagan Cushman, a jewelry designer, of Redding, Conn., Vanessa Kagan Diserio, who operates her mother’s business, of New York City, and Illya Kagan, an artist, of Nantucket, Mass.; a sister; and six granddaughters.

Among Mr. Kagan’s admirers was Zaha Hadid, the Iraqi-born architect who became the first woman to receive the prestigious Pritzker Prize, and who died one week before Mr. Kagan at age 65.

“Within each piece you can perceive a profound lightness and continuity,” Hadid once observed. “While the works of his contemporaries are definitive, finite and frozen, you experience a wonderful sense of liberation in the nonlinear, organic forms of Vladimir’s collections.”