A new simplified analytical model for penetration analysis of rigid projectiles into soil is developed. The soil medium is represented by thin plane strain discs, responding in the radial direction. The new model is based on the exact Riemann problem solution for an irreversible compressible medium. The model employs the exact nonlinear equation of state including unloading-reloading. Analysis focuses on the projectile–soil interface and predicts the projectile motion information. Very good predictions are obtained in comparison to test data and to computer code analysis.