This paper presents a novel analytical model for predicting the behavior of composite materials under three- and four-point bending tests and large deformations. The model adapts a previous isotropic formulation to account for anisotropic behavior and contact interaction. The model was validated with experimental data reported in the literature using hybrid composite materials and quasi-isotropic laminates, obtaining accurate predictions of global reaction loads, deformation, and strain measurements. Moreover, 3D shell and 2D plane strain finite element models were developed to verify the analytical model and to study the effects of large deformations on the non-linear response of composite beams. It was found that before the first drop in the load–deflection curve, most of the non-linear behavior of the investigated materials is mainly due to geometrical effects and not to damage. Finally, the implications of geometric non-linearities in the ASTM D6272 standard stress calculations were discussed, and some limitations were highlighted.