This paper deals with the identification of elasto-plastic constitutive parameters from deformation fields measured over the surface of thin flat specimens with the grid method. The approach for recovering the constitutive parameters is the virtual fields method. A dedicated algorithm is used for deriving the distribution of the 2D stress components from the measured deformation fields. A state of plane stress is assumed. Guesses of the constitutive parameters are input in the algorithm and updated until the stresses satisfy the principle of virtual work in the least squares sense. The advantage of this approach is that it can handle very heterogeneous plastic flows and it is much faster than classical finite element model updating approaches. An experimental application is provided to demonstrate it. Six mild steel double-notched specimens have been tested in a configuration combining tension and in-plane bending. The identified parameters are in good agreement with their reference counterparts. Stress fields are eventually reconstructed across the specimen all along the test for analyzing the evolution of the plastic flow.