This work was initiated because we wanted to simulate the biomechanics of the respiratory system. The main muscle that drives the respiration is the diaphragm which has an aspect ratio of approximately 1:100 of the length and thickness scales. There are several practical challenges to deal with. Creating a smooth representation of the geometry extracted from medical images; generating anisotropic scattered nodes within the thin volume; applying physically relevant boundary conditions; and solving the (non-linear) elasticity equations. In this talk, I will show results for the geometry representation as well as analysis of and results for a simplified anisotropic linear elasticity problem.