This study uses mathematical modeling to attempt to provide computational information about bioheat transfer in elastic skin tissue generated by a moving heat source that depends on different relaxation times. To achieve success in implementing heat treatment procedures, it requires a precise understanding of the heat transfer mechanism and the thermo-mechanical interaction relevant to living tissues., phase delay parameters based on relaxation times were taken into account. Due to the importance of the role of the effect of different variables on thermal relaxation times, this effect on temperature distributions, thermal stress, and displacement in living tissues was studied. Because of our use of powerful mathematical methods such as Laplace transformations and others, we were able to obtain accurate evaluations and calculations of the distributions of displacement, thermal stress, and temperature. After that, the results are given in the form of a graph for displacement, temperature, and stress. Finally, to enhance our understanding of how living tissues behave in thermal environments and to customize hyperthermia treatments, these results and a good understanding of them will do this, which will lead to improved treatment results.