The aim of this paper is to present a simple and efficient numerical technique for solving transient multidimensional heat transfer problems with melting/solidification processes. The proposed technique comprises an enthalpy-based method for solving the problems by a finite difference scheme, lump system behavior being assumed for each node. The computation technique is able to consider all kinds of boundary conditions, i.e. conduction, convection and radiation alone or in combination. The numerical method neglects convection effects in the liquid phase. The importance of this method lies in the fact that solutions are obtained with a personal microcomputer, thus providing a convenient and reliable tool for wide use in solving many problems of practical interest. The proposed method was verified against the two exact solutions available from the literature for a one-dimensional semi-infinite domain, one with constant temperature boundary condition and the second with constant heat flux. The technique was demonstrated by solving four different cases of two-dimensional problems. A comparison of the results obtained with a microcomputer using the technique presented in this paper with numerical results from the literature obtained using conventional methods, i.e. finite differences and finite elements methods, which generally involve the use of large computers, shows good agreement.