Won the Indianapolis 500 speed car race in 1937, 1939 and 1940, with average speeds of 113.580, 115.035 and 114.277 mph respectively. His speed in 1937 was a track record at the time.
Inducted into the Automotive Hall of Fame in 1987.
Shaw defied death a number of times in a race car and in 1951 survived a near fatal heart attack at the Soap Box Derby in Akron, OH, after running up the hill.
His first wife, Beatrice, died giving birth. He had a son, Warren Wilbur Shaw Jr. (born in 1945), with his second wife, Cathleen.