This work is a mathematical approach to study the temperature distribution of semi-infinite living biological tissues subject to sinusoidal heat flux on the skin with the thermal model of bioheat transfer which are often confront in cancer hyperthermia, laser surgery, thermal comfort analysis and tissue thermal parameter estimation etc.. There is equation which is known as Pennes equation that provide a relation for heat transfer between the tissue and blood has been solved with the help of Laplace transform with surface sinusoidal heating condition. This obtained solution defines the temperature distribution reactions on the surface of the skin. The results show that the temperature distribution due to the sinusoidal heating on the skin surface, it is linear initially and later on the temperature profile shows relation of temperature with respect to time when a constant heat flux is applied at the surface of the skin and it takes some finite time for skin to reach to a constant temperature.