The characteristic feature of the phase change problems is the coupling of the temperature field with the rate of propagation of the phase boundary between the solid and the liquid phases. With regarding to the nonlinear nature of these problems, the solutions are expected to be obtained by analytical approximations and numerical methods. An analytical approximate method for one dimensional phase change utilizing a new series for the temperature field in terms of the interface position is presented. Simple and accurate formulas were obtained and solved numerically by a computer program for a wide range of parameters which cover all ranges of practical systems. The resulting diagrams of the melting or solidification times for the cylinderical and spherical bodies initially at the fusion temperature are given. The boundary conditions of the first, second and third kind are considered. Evaluation of error and comparison with other approximations are presented.