This project is part of, and hence serves to support, the larger interdisciplinary project INVIVE at Uppsala University. INVIVE aims to create a biomechanical simulation of the human diaphragm. The objective of this specific project is to run deformation simulations of 3D bodies which are modeled using linear or non-linear solid mechanics. The meshfree Radial Basis Function (RBF) Partition of Unity (PUM) method (RBF-PUM) is used to create discretization matrices for the underlying equations. The linear system is then solved in a least square sense. Geometries used include thin shells of the stanford Bunny, a 3D cube with webbing and a model of the human diaphragm. Additionally, convergence studies for these problems will be conducted.