Frede Gloersen, 76, a civil engineer who helped design the first bridge across the Chesapeake Bay from Annapolis to the Eastern Shore and who later worked for the federal government, died Sunday at his home in Palm Coast. Fla., following a heart attack.

Mr. Gloersen was born in Norway and graduated from the Norwegian Technical Institute with a degree In civil engineering. He came to the United States in 1926. He worked for a railroad in the Pittsburgh area and then fo. the Pennsylvania highway department before joining the J.E. Greiner Co. in Baltimore at the end of World War II. It was while he was with the Greiner firm that he worked on the design of the Bay Bridge.

In 1957. Mr. Gloersen moved to Hyattsville and joined the Bureau of Roads in the Department of Commerce. He moved to the Department of Transportation when that agency was formed and retired to Palm Coast in 1972.

In 1971, Mr. Gloersen received an Award for Meritorious Achievement from the Department of Transportation for his work in reviewing the design of bridges on federal highway projects.

Survivors include his wife, Froydis. of the home in Palm Coast, a son, Per of Severna Park. Md., and three grandchildren.

The family suggests that expressions of sympathy be in the form of contributions to a charity of one's choice.