Schwarz methods for the mixed finite element discretization of second order elliptic problems are considered. By using an equivalence between mixed methods and conforming spaces first introduced in [13], it is shown that the condition number of the standard additive Schwarz method applied to the dual-variable system grows at worst like O(1+H/delta) in both two and three dimensions and for elements of any order. Here, H is the size of the subdomains, and delta is a measure of the overlap. Numerical results are presented that verify the bound.