The fantastic properties of polyurea such as flexibility, durability, and chemical resistance have brought it a wide range of application in various industries. Effective prediction of the response of polyurea under different loading and environmental conditions necessitates the development of an accurate constitutive model. Similar to most polymers, the behavior of polyurea depends on both the strain and strain rate. Therefore, the constitutive model should be able to capture both these effects on the response of polyurea. To achieve this objective, in this paper, a nonlinear visco-hyper elastic constitutive model is developed by the superposition of a hyperelastic and a viscoelastic model. The proposed constitutive model can capture the behavior of polyurea under compressive as well as tensile loading conditions at various strain rates. Four parameter Ogden model is used to model the hyperelastic behavior of polyurea. The viscoelastic behavior is modeled using a three-parameter standard linear solid (SLS) model. The material parameters of the model are found by curve fitting of the proposed model to the experimental data. Comparison of the proposed model and the experimental data shows that the proposed model can closely reproduce the stress-strain behavior of polyurea under a wide range of strain rates (−6500 to 294 /s).