A version of the Particle Finite Element Method applicable to geomechanics applications is presented. A simple rigid-plastic material model is adopted and the governing equations are cast in terms of a variational principle which facilitates a straightforward solution via mathematical programming techniques. In addition, frictional contact between rigid and deformable solids is accounted for using an approach previously developed for discrete element simulations. The capabilities of the scheme is demonstrated on a range of quasi-static and dynamic problems involving very large deformations. © 2013 Elsevier Ltd.