The model of two-dimensional plane waves is studied in a generalized thermoelastic medium under memory-dependent derivative in the Lord–Shulman model. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, the displacement component and the thermal stress component. The resulting formulation is applied to a concrete problem that deals with a thick plate subjected to a time-dependent heat source on each face. According to the graphical representations, corresponding to the numerical results, the effect of the different kernel has studied different thermophysical quantities at different times. Moreover, graphs are drawn to show the influence of rotation in all the thermophysical quantities. Some three-dimensional figures also are drawn for a better understanding of thermophysical quantities in the different positions of the body. As per the author’s knowledge, the effect of rotation with the memory effect is not available in the literature till now. The differences for different kernel functions are also presented at different times.