In this talk, we study three-dimensional quasi-static electroporoelasticity equations to establish a well-posedness theory and propose some numerical approximations. The electroporoelasticity model, which comprises of Maxwell's equations with Biot's equations, plays a critical role in many fields such as oil-gas exploration, water conservancy exploration, earthquake early warning and some other areas in geophysics, etc. We first apply a Galerkin method to set up the well-posedness. Then, we study a splitting finite element approximation to improve the computational efficiency. In view of distinct time scales of the development of electromagnetic waves and elastic waves, we construct a multi-time stepping numerical algorithm to accelerate numerical computations. We also investigate the numerical stability as the Lamé constant tending to infinity or the hydraulic conductivity varying randomly. Finally, we present some numerical experiments to validate all theoretical findings.