Spintronic devices are a promising beyond-CMOS device option thanks to their energy efficiency and compatibility with CMOS. To accurately capture their multi-physics dynamics, a rigorous treatment of both spin and charge and their inter-conversion is required. Here we present physics-based device models based on 4x4 matrices for the spin-orbit coupling part of the magneto-electric spin-orbit (MESO) device. Also, a more rigorous physics model of ferroelectric and magnetoelectric switching of ferromagnets, based on Landau-Lifshitz-Gilbert (LLG) and Landau-Khalatnikov (LK) equations, is presented. With the combined model implemented in a SPICE circuit simulator environment, simulation results were obtained which show feasibility of MESO implementation and functional operation of buffers, oscillators, and majority gates.