In this paper, the modeling of a polymer gel used as target medium in blunt ballistic experiments is presented. A new visco-hyperelastic law based on the Mooney–Rivlin model is proposed and implemented in a numerical simulation software. The material model identification relies on mechanical characterization experiments performed at room temperature through tensile and compressive tests over a wide range of strain rates (0.002–1500 s). Indeed, these experiments highlight a significant strain rate sensitivity but also a non-homogeneous strain and a barreling effect during compressive experiments. Hence, constitutive modeling of the material behavior cannot be directly determined. Tensile and compressive data are exploited with a direct and indirect identification process. An optimization by inverse technique, using finite element modeling of static and dynamic compressive tests and a global response surface method, is employed to accurately reproduce loading conditions and identify the model parameters. Finally, the proposed visco-hyperelastic law is validated through comparison with experimental data from blunt ballistic impacts over various projectile velocities.