Previous experimental investigations reported in the open literature have indicated that applying polyurea external coatings and/or internal linings can substantially improve ballistic penetration resistance and blast survivability of buildings, vehicles, and laboratory/field test-plates, as well as the blast-mitigation capacity of combat helmets. The protective role of polyurea coatings/linings has been linked to polyurea microstructure, which consists of discrete hard-domains distributed randomly within a compliant/soft matrix. When this protective role is investigated computationally, the availability of reliable, high-fidelity constitutive models for polyurea is vitally important. In the present work, a comprehensive overview and a critical assessment of a polyurea material constitutive model, recently proposed by Shim and Mohr (Int J Plast 27:868-886, 2011), are carried out. The review revealed that this model can accurately account for the experimentally measured uniaxial-stress versus strain data obtained under monotonic and multistep compressive loading/unloading conditions, as well as under stress relaxation conditions. On the other hand, by combining analytical and finite-element procedures with the material model in order to define the basic shock-Hugoniot relations for this material, it was found that the computed shock-Hugoniot relations differ significantly from their experimental counterparts. Potential reasons for the disagreement between the computed and experimental shock-Hugoniot relations are identified.