Perturbation solutions for the phase-change problem during solidification involving the wall conduction and wall-material interfacial thermal contact resistance boundary condition are presented in a straightforward approximate analytical manner. Comparison is made between the present result and those in the case with neglecting the effects of wall-material interfacial thermal resistance and/or wall conduction. It is found that the solidification rate increases with decreasing wall-material interfacial thermal resistance, or increasing Stefan number, or decreasing the ratio of solidified-material thermal conductivity to wall thermal conductivity.