The phenomenon of irregular shock-wave reflection is of importance in high-temperature gas dynamics, astrophysics, inertial-confinement fusion, and related fields of high-energy-density science. However, most experimental studies of irregular reflection have used supersonic wind tunnels or shock tubes, and few or no data are available for Mach reflection phenomena in the plasma regime. Similarly, analytic studies have often been confined to calorically perfect gases. We report the first direct observation, and numerical modeling, of Mach stem formation for a warm, dense plasma. Two ablatively driven aluminum disks launch oppositely directed, near-spherical shock waves into a cylindrical plastic block. The interaction of these shocks results in the formation of a Mach-ring shock that is diagnosed by x-ray backlighting. The data are modeled using radiation hydrocodes developed by AWE and LANL. The experiments were carried out at the University of Rochester’s Omega laser [J. M. Soures, R. L. McCrory, C. P. Verdon et al., Phys. Plasmas 3, 2108 (1996)] and were inspired by modeling [A. M. Khokhlov, P. A. Höflich, E. S. Oran et al., Astrophys J. 524, L107 (1999)] of core-collapse supernovae that suggest that in asymmetric supernova explosion significant mass may be ejected in a Mach-ring formation launched by bipolar jets.