The objective of this paper is to develop an accurate and efficient solution procedure for elastoplastic problems in structural mechanics in the framework of a two-field mixed variational principle. A novel solution algorithm is proposed and applied to the elastoplastic analysis of Mindlin plates. The Hellinger-Reissner principle is adopted to obtain the global finite-element equations of the problem. Instead of a static condensation, the stress-type field variables are preserved during the solution. According to the proposed approach, the strain increments within a nonlinear solution step are obtained directly at the nodal points from matrix operations instead of gradients of a displacement field. In the present implementation, the von Mises yield criterion with linear hardening is adopted. For the integration of the elastoplastic constitutive rate equations at the nodal points, a 3D fully implicit algorithm is employed. A layered approach is followed to enable the resolution of the plastic strains through the plate thickness. The mixed formulation of the Mindlin plate theory is shear-locking free by construction. The proposed solution strategy is verified by solving several benchmark problems that demonstrate the high accuracy and convergence rate of the presented layered mixed formulation for elastoplastic analyses.