Analysis of a Stefan-like problem in the in vivo freezing of a biological tissue is presented in cartesian coordinates. The analysis allows the inclusion of blood perfusion, metabolic heat and tissue heat capacity. Solutions are obtained for the temperature distributions in the frozen and unfrozen regions at different times. A constant freezing rate, in accordance with the optimal tissue destruction rate, is assumed. Results indicate the importance of the blood perfusion factor in the problem and allow the prediction of probe temperature and heat flux variations for optimal results in tissue destruction.