This paper presents the formulation and numerical implementation of a physically nonlinear BDM element for plane stress. The BDM element is based on the dual extended Prange-Hellinger-Reissner functional. We discuss in detail, the linearization of the extended functional needed for solving the system of nonlinear equations with a Newton procedure. In the case of elasto-plasticity at small strains, the weak form is modified to fulfill the kinematical field equations. The Euler-Lagrangian equations satisfied approximately in the discretized form are pointed out. A concept for the storage and update of the internal variables is shown in detail. For two specified model problems, nonlinear elasticity and von Mises plasticity with linear hardening, numerical examples are given.