This study aims to develop the analytical solution to the phase change heat transfer process in biological tissue undergoing cryosurgery. Cryosurgery is a clinical procedure for treating cancer by exposing the tumor tissues to cryogenic temperatures. Studying the heat transfer process in the living tissue during cryosurgery can provide insights on how to optimize the several parameters of the process and how to judge the effectiveness of the process. Tracking the thermal history of the tumor tissue and healthy tissue and monitoring the freezing front propagation can help maximize damage to cancer cells while minimizing damage to surrounding healthy tissue. Involvement of phase change in the heat transfer process means the formation of a phase change interface. Previous studies have used numerical schemes that are computationally intensive since the temperature field, and the interface position are linked by non-linear parital differential equations. This study proposes a novel approach using the coordinate transformation technique to reduce the non-linear partial differential equations into ordinary differential equations. Firstly, a solution to the 1-D Stefan problem is obtained and verified with previous results. Next, the Pennes bio-heat transfer equation is solved with the isothermal phase change, and the results are presented. The results agree satisfactorily with previously published work, and the computational time and resources required are negligible.