Cryoablation, a minimally invasive technique for treating cancer, could benefit from computer support in planning, intervention and follow-up. For employing such treatment planning in daily clinical routine, individualized simulation of cryoablation needs to be sufficiently accurate and fast. This paper describes a simulation of cryoablation of human kidney permitting high-performance simulations on graphics hardware. The simulation involves partial differential equations modeling temperature evolution and phase changes in the tissue, as well as equations describing the dependence of tissue parameters on tissue temperature. A mushy region approach and a predictor-corrector time stepping scheme are utilized for discretization to achieve an efficient numerical scheme implemented on graphics hardware. The simulation is planned to be integrated in an approved medical device.