An elastic‐plastic constitutive model to describe the nonlinear compressive stress‐strain behavior of fiber reinforced polymer composites was developed under the plane stress condition. Model predictions are based on the tensile properties and a tensile/compressive asymmetry coefficient. A variety of tensile and compressive tests were carried out on 0°, 15°, 45°, and 90° unidirectional and ±30° and ±45° angle‐ply thermosetting and thermoplastic polymer composite laminates to obtain the material parameters and validate the model, while the finite element implementation and applications to three‐point bending loading are discussed in the next investigation.