Paul Lynde, who was a regular performer on the television game show ''The Hollywood Squares,'' died, possibly of a stroke, Saturday at his home. The actor was 55 years old.

Mr. Lynde had a leading role in the 1960 Broadway play and the 1963 film version of ''Bye Bye Birdie. Reviewing the show, Brooks Atkinson, drama critic of The New York Times, wrote, ''Paul Lynde contributes to the merriment of the nation by simulating indignation and provincial fatuity.''

Mr. Lynde made his Broadway debut in 1952 in ''New Faces,'' gaining attention for his mon ologue, ''The African Explore r,'' which he wrote. His other stage appearances included ''New Faces of 1956,''for which he served as playwright and director, and ''New Faces of 1962,'' where he again received credit as playwright. Outs ide New York, he played leading roles in ''Visit to a Small Planet '' and ''Panama Hattie.'' Some of His Film Credits

In Hollywood, he appeared in ''Son of Flubber,'' ''Under the Yum Yum Tree,'' ''For Those Who Think Young,'' ''Send Me No Flowers,'' ''The Glass Bottom Boat,'' ''How Sweet It Is'' and ''The Villain.''

Mr. Lynde also starred in ''The Paul Lynde Show'' on television and made regular appearances on the ''Jonathan Winters Show,'' ''Dean Martin Presents'' and on most of the variety and talk programs. He also made nightclub appearances.

The actor was born in Mount Vernon, Ohio, on June 13, 1926, and attended Northwestern University, where he majored in drama and speech. After graduation, he moved to New York and worked at odd jobs until he began his career as a stand-up comedian at Number One Fifth Avenue.

Mr. Lynde, who was unmarried, is survived by a sister, Helen Lynde of Los Angeles.

Interment Amity Cemetery, Knox County, Ohio.