Efficient computational modelling of problems including both material and geometric nonlinearities remains challenging. Often these problems are modelled with adaptive finite element method (FEM). Meshless methods offer the attractive possibility of simpler adaptive procedures involving no remeshing, simply insertion or deletion of nodes. In this study an adaptive meshless approach for nonlinear solid mechanics is developed based on the element free Galerkin method. An existing error estimation procedure for linear elasto-static problems, is extended here for nonlinear problems including finite deformation and elasto-plasticity, and a new adaptive procedure is described and demonstrated.