One of the main challenges in developing the hydrogen infrastructure is the distribution and storage of hydrogen. A common method to store hydrogen is as a compressed gas. Electrochemical compression (ECC) is a promising technology that can sidestep some of the disadvantages present in conventional mechanical compressors. ECC is an externally powered device that employs an electrochemical cell containing a polymer electrolyte membrane (PEM) to compress the gas. This work presents a detailed 2D ECC model developed using COMSOL Multiphysics 5.6, that considers the important phenomenon of back diffusion resulting from the high pressure differential between cathode and anode during compression. Results from the current simulations are validated against experimental results obtained previously in our lab. Simulations were first conducted for the unpressurized cathode and the performance was analyzed in terms of the polarization curve. Next, simulations were conducted for the pressurized cathode, with and without considering back diffusion. In the absence of back diffusion, the pressure ratio reaches the value predicted by the Nernst equation. However, the presence of back diffusion greatly reduces the pressure ratio similar to experimental observations.