AbstractWe describe a new version of the moving particle finite element method (MPFEM) that provides solutions within a C0 finite element framework. The finite elements determine the weighting for the moving partition of unity. A concept of ‘General Shape Function’ is proposed which extends regular finite element shape functions to a larger domain. These are combined with Shepard functions to obtain a smooth approximation. The Moving Particle Finite Element Method combines desirable features of finite element and meshfree methods. The proposed approach, in fact, can be interpreted as a ‘moving partition of unity finite element method’ or ‘moving kernel finite element method’. This method possesses the robustness and efficiency of the C0 finite element method while providing at least C1 continuity. Copyright © 2004 John Wiley & Sons, Ltd.