A nonlinear elastic-inelastic model for a thermosetting polymer is proposed based on the molecular chain network theory. In the proposed model, the bond of the polymer chain is divided into physical and chemical bonds, and the physical bond is allowed to separate and recombine during the deformation. The decrease in the rigidity and increase in the inelastic strain are related to the development of the physical bond density to represent the characteristic deformation behavior of the polymer. A rate-form large deformation constitutive equation is then formulated based on the updated Lagrangian method. Additionally, deformation behaviors of the epoxy under monotonic and cyclic tensile tests were evaluated by experimental and computational studies. The experimental results of the monotonic tensile test displayed a gradual transition from elastic to inelastic deformation, strain softening behavior after the macroscopic yielding stress, and an increase in the initial slope and the macroscopic yielding stresses with an increasing strain rate. The computational model can represent such characteristics by controlling the development of the physical bond density. In a cyclic test, a decrease in the rigidity and an increase in the residual strain with increasing cycles were observed even in a small strain range. Such inelastic deformation depended on the strain rate and the given upper stress in the cyclic test. Further, the proposed model successfully reproduced such nonlinear behavior in the cyclic test.