This work examines the constrained recoil after steady shear flow and the free recovery after steady elongational flow of monodisperse polymer melts. Calculations are performed in the framework of the Curtiss-Bird theory using both conventional numerical integrations and nonequilibrium Brownian dynamics. The latter approach is shown to have significant advantages, particularly at high shear or elongational rates. The predicted curves of recovery as a function of shear rate exhibit an unusual maximum for which several explanations are proposed.