Simulation results on three-dimensional freezing phenomena around a cryoprobe are presented in the manuscript. Both fixed-grid explicit and implicit schemes based on the effective heat capacity method have been employed to solve the system of governing equations. The study revealed that the grid size of 1 mm and less is adequate to model the freezing process in the cryosurgical applications. Based on this study, an explicit solver was employed for the detailed solution of the governing equations. A stair-step approximation was used to model the cylinder-shaped cryoprobe geometry in three-dimensional space. Results of numerical simulations have been benchmarked with the exact solution, in vitro as well as in vivo experimental studies were reported in the literature. The results of the present study showed that the temperature-dependent thermophysical properties lead to better accuracy in temperature predictions inside the biological tissue. The effect of convective heat transfer to ambient was found negligible for deeper cryoprobe placements. The necrotic region engulfed by the lethal -50°C temperature (isotherm) is located approximately midway between the cryoprobe and the solid boundary of 0°C. The maximum tumor volume treated by any cryoprobe could be obtained a priori by performing the transient analysis as carried out in the present study.