Biaxial extensional flow behavior of polystyrene and polypropylene melts was measured utilizing the lubricated squeezing flow method under the condition of constant strain rate. The uniaxial extensional flow behavior of these samples was also measured using a Meissner‐type rheometer for comparison with the biaxial behavior. The biaxial stress growth coefficient ηB+grows more slowly than the uniaxial stress growth coefficient ηE+at long times. Deviation of ηB+from the low strain rate asymptote is not so prominent as that of ηE+. The deviation of ηB+and the upturn of ηE+from the low strain rate asymptotes are more apparent in broad distribution samples than in a narrow distribution sample. It is found that ηB+decreases with strain rate at long times near steady state. The upturn behavior of ηE+at high strain rates in a narrow distribution sample is discussed based on the Doi–Edwards theory and stress relaxation data. The upturn is clearly observed when the strain rate exceeds the contraction (retraction) rate τeq−1, where the contraction time τeqis evaluated from the relaxation data. Consideration on chain stretching in various multi‐axial extensional flows gives a prediction for deviation of stress growth coefficients from the low strain rate asymptotes in uniaxial, biaxial, planar, and ellipsoidal extensional flows.