The Green Element Method (GEM) is a new, powerful, and promising technique for solving boundary value problems which arise in many engineering applications such as flow in aquifers, heat transfer processes and electro-magnetic field problems. The method has proved to be very effective in handling heterogeneity and anisotropy in 1D and 2D domains, but the development of techniques to implement the Green Element Method in 3D domains has remained largely elusive because of many challenges including the domain integrations and the compatibility issues that arise between element faces. This work represents an implementation of GEM for steady and time-dependent problems using regular tetrahedral and hexahedra elements.