Tissue freezing has significant applications in cryopreservation and cryosurgery processes. The freezing rate is an important factor during the cryopreservation process. To improve and make an accurate estimation of the freezing rate, radiation heat transfer plays a major role. To analyze in details, a two-dimensional coupled conduction–radiation model is developed. The tissue is frozen from the left side while the other sides are at the initial temperature. Finite volume method (FVM) is used to discretize both the radiative transfer equation (RTE) and energy equation. The algebraic equation after discretization is solved by the tri-diagonal matrix algorithm. The radiative heat flux is calculated by solving the RTE. The energy equation provides the temperature field. The enthalpy-porosity method is used to update the liquid volume fraction and thus the freezing front is captured. A linearization technique is proposed to linearize the radiative source term in the energy equation to avoid chances of divergence of the solution. The present model is first validated with the results of the existing literature and a good agreement is found. The effects of different parameters such as conduction–radiation parameter, scattering albedo, extinction coefficient and Stefan number on the prediction of temperature field, and the position of the freezing front are studied in details. It is found that a decrease in the values of conduction–radiation parameter, scattering albedo, and increase in the values of extinction coefficient and Stefan number cause more radiative heat loss. Hence, the freezing rate is improved and more frozen region is observed.