New criteria for testing integral constitutive equations are proposed. The constitutive models studied are generalized models with stress‐, strain‐, and rate‐dependent memory functions, as well as the BKZ and Bogue‐White (BW) models. On the basis of these models, the critical relations for the test of constitutive equations are derived for five types of experiments: single‐ and double‐step stress relaxation under finite shear strain, stress overshoot, interrupted flow, and stress relaxation after cessation of steady shear flow. Among the models examined in this study, the predictions as to the time‐dependent stress or relaxation modulus in single‐ and double‐step stress relaxation are quite different, and therefore these relaxation experiments are very useful for testing the models. The Van Es‐Christensen function is monotone increasing in time for strain‐dependent models as well as for rate‐dependent models. On the other hand, it is possible that the function overshoots for the stress‐dependent model. New critical tests are proposed using interrupted flow. It is demonstrated that relations between shear and normal stress relaxation after cessation of steady shear flow are very useful for testing the models.