The nonclassical heat conduction equation based on the Maxwell-Cattaneo-Fox (MCF) model is used to study the Stokes’ first and second problems for the Rivlin-Ericksen fluids. The discontinuities in velocity gradients in fluid flows induced by impulsive or sudden heating of a plate and the influence of the thermal relaxation time and elastic parameter of the fluid on the velocity field are investigated. The structure of the waves in the temperature and velocity fields is presented. An anomalous behavior of the medium is characterized by infinite or negative values of the group velocity for the wave packets as the frequency attains or exceeds a critical value. The displacement thickness and the rate of heat transfer at the plate are determined.