The adiabatic compression of plasmas with mass rotation is formulated as a variational principle based on some constants of the motion. A numerical code is constructed and Grad’s alternating dimensions method is used. The calculations simulate compression either by increasing the flux outside the plasma or by liner compression. Changes in Mach number and some stability criteria during compression are monitored. Interestingly, the Mach number remains almost constant despite a spin up of the plasma. An extension of the interchange stability criterion for rotating plasmas is developed. Interchange stable equilibria exhibit very high current density near the separatrix and tend to be more elongated. Interchange instability offers a mechanism to generate rotation throughout the plasma.