This paper presents a computational procedure to simulate the time-domain behavior of photoconductive antennas made of semiconductor and metal materials. Physical modeling of semiconductor devices at terahertz regime can be achieved by applying joint electronic and electromagnetic procedures, e.g., solving a coupled system of equations inferred from Poisson's drift-diffusion and Maxwell's equations. A set of discrete equations are derived by applying a combined finite-difference methodology for the previous steady-state and the finite-difference time-domain procedure for the transient regime. The results for the radiated electric field at broadside direction show good agreement with the experimental results previously reported in the literature.