Mechanical structures are widely analysed by means of numerical simulators developed based on physical laws. In the context of structural mechanics, while the formulations of both kinetics and kinematics are transparently established in accordance with Newton’s laws and the compatibility condition of deformation, the constitutive relation often suffers from a considerable amount of uncertainties. Such uncertainties are mainly rooted in insufficient physics and imprecise assumptions and simplifications. In recent decades, Bayesian techniques have been utilized for coping with these uncertainties and for quantifying the level of confidence that may be attributed to the inferred model. Among various approaches, some of which are reviewed in [1], this work focuses on the parameter identification of a candidate parameterized physics-based constitutive model, on the basis of full-field measurements of displacements. These measurements are assumed to be obtained in the form of Digital Image Correlation (DIC) measurements, complemented with external force measurements at the structural level aggregated over certain sub-boundaries. The principal idea is to minimize a suitable objective function that measures the discrepancy between the parameterized model’s response and the measured quantities. This objective function is formulated in terms of the internal forces and the measured aggregated forces, and the associated Bayesian inverse problem is introduced. A variational Bayesian scheme, originally proposed in [2], is employed to compute the unknown posteriors considered as multivariate normal distributions. We verify our framework on two synthetic examples described by a gradient damage model [3] and an elastic law, with the former reflecting a path-dependent nonlinear constitutive law. The first example illustrates an application of the proposed procedure to cracked structures. In the second example, a regularizer, in terms of admissible stresses, is further incorporated to the identification procedure, offering robustness against contamination of measurements with noise.