The main objective of our research is to understand the functionality of a human diaphragm, the main muscle of the respiratory system. Its action affects the volume of the thorax cavity such that the lungs can inflate and deflate, enabling a human to breathe. The aim is to enable medical researchers to perform studies on ventilator induced diaphragm disease (VIDD). The diaphragm models in the existing simulation tools are not advanced enough to capture the processes that lead to VIDD. Our model is based on the nonlinear elasticity equations. The goal is to solve the equations on a 3D diaphragm geometry. That can exhibit some numerical difficulties related to the small thickness of the tissue, compared to the overall size of the muscle. Localized radial basis function methods are chosen to discretize the equations in space and the quasistatic approach is used to advance the movement of the diaphragm in time. In this talk we will present the results of our first steps. These include the solutions of the static linear elasticity equations on a simple thin-plate geometry and also the full diaphragm geometry.