Mathematical modeling of an Electric-Swing Adsorption (ESA) system (adsorption cycle with electrothermal desorption step, performed by direct heating of the adsorbent particles by passing electric current through them), with annular, radial-flow, cartridge-type fixed-bed and invessel condensation, is performed by using Comsol Multiphysics™ software. Three multiphysics models are built, in order to describe three stages of a compete ESA cycle: adsorption, electrothermal desorption before the start of condensation and electrothermal desorption with in-vessel condensation. In order to describe the complete ESA cycle the models for the three stages are integrated, by using a combination of Comsol Multiphysics™ and Matlab™. The models were successfully used for simulation of separate stages of the process and of the complete ESA cycles, as well as for investigation of the influences of the main operational parameters on the process performance.