The time‐dependent shear and normal stresses arising in polymeric fluids during multistep‐shear deformations have been modeled using the Leonov constitutive theory. An analytical solution of the problem has been obtained. The model parameters for the materials have been determined from the experimental time‐dependent linear relaxation modulus in a single‐step shear. The results based upon the present theory have been compared with the experimental data obtained by Osaki and co‐workers for different polystyrene solution in double‐step‐shear deformation in the nonlinear region and also with theoretical results based upon the Doi‐Edwards and the BKZ theories. The present theory shows good agreement with the experiments, including the strain histories for which the above‐mentioned theories show discrepancies.