in this thesis we conduct an examination of pyramidal elements and their use as interface, or mortar, elements in the joining of tetrahedral and hexahedral elements in three dimensional finite element meshes. several new sets of basis functions are developed and analyzed for pyramidal elements having five, thirteen and fourteen nodal points. these basis functions take advantage of the symmetries of the element in order to give improved accuracy over previously studied basis functions. evidence of this improvement in accuracy is presented in the form of numerical experiments.