A moving mesh approach is employed to simulate two-phase flow with phase change. The mathematical model is based on the Arbitrary Lagrangian-Eulerian (ALE) description of the axisymmetric Navier-Stokes equations and energy conservation. These equations are discretized by the Finite Element Method (FEM) on a triangular unstructured mesh in which the phase boundary is represented by a set of interconnected nodes and segments that are part of the computational mesh. Here, phase change and surface tension are implemented as source terms, using the one fluid approach. The method is shown to provide an accurate description of the interfacial forces, heat and mass transfer between phases. Several different verifications are presented where the results are compared to analytical and semi-analytical solutions. (C) 2018 Elsevier Inc. All rights reserved.