The edged-based functions for a distorted triangular prism are derived and validated. The distorted triangular prism allows for meshes that are unconstructed in two dimensions and structured in the third dimension. This simplifies the meshing algorithm and many printed antenna and microwave circuit geometries that are easily tessellated using such a mesh. The new edge-based shape functions presented are validated by computing the eigenvalues of three different cavities: rectangular, cylindrical, and pie shell.