We have developed a numerical model for simulating the deformation behavior of elastic sheet materials based on the moving finite elements (MFE). The MFE is a variant of adaptive grid methods, which automatically relocates the grid of nodes on the surface while computing its deformation. When relocating the nodes, the MFE tries to minimize the discretization error of the surface representation. Therefore, the nodes tend to gather at sharply curved or high curvature regions on the surface. This property has been found to be suitable for simulating the creasing phenomena observed on nearly unstretchable sheet materials.