In medical world, the minimally invasive freezing therapy or cryosurgery is an efficacious treatment for complete and controlled eradication of tumor cells. Many difficulties are encountered in cryosurgery process such as inappropriate freezing may not completely destroy the target tumor tissue and excessive freezing may harm the surrounding healthy tissues due to release of high amount of cold from the freezing probe. In present study, the target tumor tissue is loaded with nanoparticles in order to improve the freezing capacity of probe and to regulate the orientation and size of ice-ball formed during cryosurgery. In this process, phase transformation occurs in the undesired tumor tissues. For simulation of phase transition in bio heat transfer equation, the fixed-domain, heat capacity method is used to take into account the latent heat of phase change. In this study, a meshfree numerical technique known as element free Galerkin method (EFGM) is employed to simulate the phase transition and temperature field for a biological tissue subjected to nanocryosurgery. The latest nanofluid model which includes the effects of particles size, concentration, and the interfacial layer at the particle/liquid interface is utilized and their impact on freezing process is investigated in detail.