Assessing magnetohydrodynamic stability of the envisaged scenarios for the operation of a new tokamak is of primary importance for machine performance and safety. COMPASS Upgrade (COMPASS-U) is a compact tokamak which is being built at the Institute of Plasma Physics in Prague; COMPASS-U will explore various plasma scenarios, characterized by different magnetic fields, plasma currents and plasma shapes. Systematic stability calculations with MARS-F code (Liu et al 2000 Phys. Plasmas7 3681) were performed on the main representative scenarios for COMPASS-U operation and the most unstable modes were identified. The considered scenarios were found to be unstable to internal kink modes, which implies the presence of sawtooth activity. On the other hand, the nominal β (ratio of the volume-averaged plasma pressure to the magnetic pressure) of the scenarios is below the no-wall limit for stability to external kink modes. The main scenarios, characterized by , are stable with respect to tearing modes for nominal β because of the stabilizing Glasser–Greene–Johnson effect, while scenarios with are expected to be unstable for finite β. The stabilization produced by an ideal wall placed close to the plasma suggests that the finite-β destabilization is caused by coupling to pressure-driven external modes. A preliminary assessment of stability with respect to pressure-driven modes was attempted. Stability with respect to neoclassical tearing modes (NTMs) was assessed by using generalized Rutherford equation; stabilization of NTMs by electron cyclotron heating and current drive was evaluated.