This paper investigates the dynamic spherical cavity expansion of shock wave evolution in concrete medium described by compressible Drucker–Prager plasticity with locked hydrostat. Hugoniot jumping conditions across shock waves are fully accounted for and a complete description of the motion and stress distribution evolution is obtained for different response domains. By solving the dimensionless governing differential equations during different periods, numerical illustrations are then developed with application to an explosion scenario inside an infinite concrete medium. The parameter study indicates that the equivalent charge weight of TNT proportionally affects the shock waves evolution, while the standoff distance has an inversely proportional impact on the ultimate locked/compacted boundary area.