A hybrid model treating electrons as a dissipative fluid and ions as particles is used to investigate numerically the properties of high-Mach-number magnetoacoustic shock waves propagating perpendicular to a magnetic field. Upon increasing the Alfvén Mach number MA, the electron pressure behind the shock becomes bounded for MA ≳ 15. Ion reflectivity a increases but stays rather small even for MA → ∞, B0 → 0 (i.e. α = 30 – 40% for reasonable collision frequencies in the shock). Thermalization of the plasma by multiple bouncing in a cylindrical tube is studied for the case where the ion gyroradii are large compared to the tube radius. Strong damping is found to lead to equilibration after about two bounce oscillations. Ion reflection during the first implosion is found to be essential for non-adiabatic ion heating in the succeeding thermalization period.