In the present manuscript, a two-dimensional generalized thermoelastic model is used to study the problem of reflection of thermoelastic plane waves from a stress-free and thermally insulated boundary of thermally conducting isotropic homogeneous elastic material. The Lord–Shulman model under the heat transfer law with memory-dependent derivative is employed to model this problem. The case of total reflection is taken into account to calculate the critical angle. Phase velocities and corresponding attenuation factors of the coupled dilatational elastic-thermal waves and the ratios of the reflection coefficients are calculated and illustrated graphically for copper-like material and highlighted the effects of various parameters of interest. © 2020, Indian Association for the Cultivation of Science.