This article discusses the application of the MLPG method to phase change problems. Phase change problems belong to a nonlinear class of problem due to a continuously moving interface. Apparent capacity method based on the enthalpy formulation is used here. The method of direct interpolation is employed to enforce essential boundary conditions. Function approximation is completed by using the moving least squares (MLS) method. An iterative procedure based on the predictor-corrector method has been used to handle nonlinearity. Time integration has been performed using the -method. Results have been compared with the available exact solution and the solution of the finite element method, and found to be in good agreement. Copyright © Taylor & Francis Group, LLC.