A simple approximation for predicting the concrete erosion rate and depth is derived based on the heat balance integral method for conduction with the time-dependent boundary conditions. The problem is considered a four-region model including separate, moving heat sinks at the boundaries due to endothermic decomposition reactions. Polynomial temperature profiles are assumed, and the results are compared with previous experimental data and other analytical solutions. Since the technique provides an approximate temperature distribution on the average, it does not give the real temperature evaluation but provides a simple prediction of the erosion rates and the depth of defaulted concrete in terms of the parameters that are important during the physical phenomena. Because of its simplicity and reliability, the model might be useful for the larger molten core/concrete interaction codes and aerosol generation models.