Freezing processes taking place in a plate, a cylinder and a sphere are investigated by using the improved quasi-steady analysis model developed in the present study. In the improved quasi-steady analysis, an additional term is added to the temperature profile to simulate the transient effect on the temperature distribution in the solid phase. This additional term is based on the ratio of the heat flux at the phase boundary to that at the cooling surface, and physically, presents the thermal capacity effect in the frozen region. The maximum relative error of the moving phase front location obtained from the improved quasi-steady analysis is about 3% in comparison with that obtained from the exact solution of the freezing process in a plate. Since there is no exact solution available for the freezing process taking place in a cylinder or a sphere, the results obtained from the improved quasi-steady analysis are compared with results from references. The maximum relative errors of the improved quasi-steady analysis for the cylindrical and spherical cases are less than 4% while the maximum relative errors of the quasi-steady approximation are higher than 42%. It is evident that the improved quasi-steady analysis developed in the present study maintains the simplicity of the quasi-steady approximation while greatly increasing its accuracy.