The role of the normal stresses in laminar boundary layer flow of viscoelastic fluids past submerged bodies is analyzed. The second‐order equation is assumed for the fluid. The results show that the first normal stress difference tends to shift the fluid separation toward the front stagnation point. This analytical result contradicts previous experiments, which showed that the elasticity of the fluid retards the fluid separation. On the other hand, similar analysis, based on a different constitutive equation, shows that the stress relaxation effect in elastic fluids retards the separation point and reduces drag, in agreement with experimental trends. These results suggest that stress relaxation is a more dominant effect, compared to the normal stresses, in laminar boundary layers at high Reynolds' numbers.