A fundamental microstructural model was developed to calculate the stress-strain curves of rubbery amorphous polymers and of semicrystalline polymers with a rubbery amorphous phase by numerical simulations. The rubbery amorphous phase was treated by using a version of the theory of rubber elasticity with finite extensibility. Physical entanglements and chemical crosslinks were both allowed. Slippage was implemented by a Monte Carlo algorithm controlled by kinetic parameters such as the activation energy and activation volume for slippage. The crystalline phase was treated in a very idealized manner, including a crude representation of tie chains but not taking the internal structure of the crystallites into account. A two-dimensional embodiment of the model was implemented into software. For amorphous polymers, while lacking truly quantitative accuracy, the model showed sufficiently good agreement with the experimental trends to be used as a qualitative or semiquantitative predictive tool, and it is currently being used in this manner. The more complex semicrystalline version was less accurate and will need to be improved in future work. Most of the limitations of the semicrystalline version could be ascribed unambiguously to specific simplifications made in the software implementation to reduce the amount of computer time required for the calculations.