Summary: In this paper we construct a fully compatible staggered Lagrangian algorithm for the equations of two-dimensional elastic-plastic flows (FCSLAEP), with the hypo-elastic incremental constitutive model, von Mises’ yielding condition and the Mie-Grüneisen equation of state. To construct our scheme, we first reformulate all governing equations of elastic-plastic flows, including the equations of deviatoric stress, into a hyperbolic system in the form of the divergence and the gradient operators. Then, this hyperbolic system is discretized by adapting the method of support operators and using some new vector identities of differential calculus. Moreover, we replace the finite volume surface integrals with the line integrals and rewrite the equations of deviatoric stress in the form of the internal energy on the right-hand side (so that one can use the gradient operator on the velocity in the discrete form), to discretize the equations of deviatoric stress in order to conserve the total energy and preserve the symmetry. Finally, the predictor-corrector technique is used with respect to time to improve the accuracy. A number of numerical tests are carried out, and the numerical results show that the proposed scheme FCSLAEP seems robust and convergent. Moreover, the scheme is of the 2nd order accuracy, and conserves the total energy and preserves the symmetry.