[en] Analytic regularization for the Casimir Effect for rectangular systems in one^-, two^- and three-dimensions, as well as for parallel conducting plates, is discussed. We consider the analytic regularization by employing the Riemann zeta function as well as the zeta functions introduced by Epstein. The forces, in this case, come out automatically finite, i.e., no subtractions are needed. We show that the analytic continuation, in the number of imaginary time dimensions, corresponds to introducing generalized zeta functions for the zero point energy