Constitutive model identification schemes such as “force-based Finite Element Model Updating” (FEMU-F) and “Equilibrium Gap Method” (EGM) aim to minimize a cost function expressed in terms of FE force residuals after imposing measured full-field displacements as Dirichlet constraints. However, the loss functions of such force-based approaches are known to be sensitive to noisy displacements [1,2]. This work proposes a robust, regularized force-based cost function that operates directly on elemental internal forces without assembling these into nodal values. The proposed scheme introduces admissible elemental internal forces (AEIFs) as additional unknown variables into the inverse formulation, which act as a regularization mechanism. By definition, AEIFs satisfy static equilibrium with external forces, independently of kinematics and constitutive assumptions. The proposed cost function measures the discrepancy between AEIFs and the elemental internal forces predicted by the FE model. Numerical examples are presented to demonstrate the regularization effects of AEIFs in reducing sensitivity to noisy full-field displacements and inaccurate Dirichlet boundary conditions. In addition, the proposed method exhibits robustness in capturing material properties in areas far from the measured forces. It enables more accurate identification of heterogeneous elasticity than FEMU-F using a single measured integrated force. The method remains robust in the identification of damage parameters in the presence of strain localization, underscoring the suitability of force-based identification approaches for such challenging material behaviors [3]. [1] S. Avril, F. Pierron, General framework for the identification of constitutive parameters from full-field measurements in linear elasticity, International Journal of Solids and Structures, 44, 4978–5002, 2007. [2] M. Flaschel, S. Kumar, L. D. Lorenzis, Unsupervised discovery of interpretable hyperelastic constitutive laws, Computer Methods in Applied Mechanics and Engineering, 381, 2021. [3] A. Jafari, K. Vlachas, E. Chatzi, J. F. Unger, A bayesian framework for constitutive model identification via use of full field measurements, with application to heterogeneous materials, Computer Methods in Applied Mechanics and Engineering, 433, 117489, 2025.