An electrorheological gel (ERG) is a functional material that changes its surface adhesive property according to the intensity of the applied electric field. It is a composite material consisting of ER particles and silicone gel. Under no electric field, the surface adhesion is low because the slippery ER particles protrude from the gel surface. When an electric field is applied to an ERG, silicone gel around ER particles rises and covers the ERG surface such that the surface adhesion becomes high. The surface adhesion of ERGs can be changed quickly and reversibly by adjusting the electric field. This unique property is called the electro adhesive (EA) effect. However, although this electro adhesive phenomenon has been experimentally confirmed, the physical theory has not been sufficiently developed. In this study, the theory of the EA effect based on electromagnetics is developed and validated using a numerical analysis. Simulation results show that ER particles sink into silicone gel, and silicone gel around ER particles heaves due to the Maxwell stress and gradient force of the applied electric field.