The Riemann problem for an irreversibly compressible three-phase medium has been solved. This solution introduces the maximum medium density that is attained in the process of active loading. The possible wave configurations have been analyzed, and the corresponding equations for the evaluation of the contact pressure and velocity have been obtained. The existence and uniqueness of the solution has been proven. The technique of the Riemann problem's solution for the arbitrary Lagrange–Euler mesh was developed. Examples of the Riemann problem solution for various wave configurations show that neglecting the bulk elastic plastic deformations yields significant errors in the results both quantitatively and qualitatively. The effect of the air volumetric content in a three-phase soil medium on the Riemann problem solution has been investigated. Copyright © 2013 John Wiley & Sons, Ltd.