Abstract: The finite particle method (FPM) is new numerical method and suitable for analyzing structures and mechanisms undergoing large rigid body motion, deformation or their coupled problems. FPM has been successfully applied to infinitesimal mechanisms, deployable structures, contact, progressive collapse, buckling, cable-strut structures, 2D solid, membrane structures, multi-scale analysis and refinement analysis. In order to form a complete FPM research scheme involving 2D and 3D solids and elastic-plasticity problems, a constant strain 3D tetrahedron solid element was proposed in this study, and the formulations of internal forces were derived. Additionally, an elastic-plasticity analysis was also conducted. Several numerical examples with behavior of static, dynamic, nonlinear material properties were presented to demonstrate the performance and applicability of the proposed approach. Compared with the nonlinear finite element method (NFEM) and experiments, the results of numerical examples solved by self-designed program show that the present method is of high level of reliability and accuracy.