The fine balance of the horizontal and vertical sweeps of the standard alternating direction implicit method is efficiently incorporated in the numerical scheme for the two-dimensional phase change problems. The present method isolates the non-linearity associated with the moving interface and accurately tracks the interface movement along both the coordinate axes. This avoids the need for iterations at ordinary nodes away from the interface. Numerical results are obtained and plotted for square and rectangular prisms undergoing phase change. © 1984.