Ideal MHD stability calculations for the ARIES compact stellarator (ARIES-CS) reactor design (Najmabadi et al 2008 Fusion Sci. Technol.54 655) show a spectrum of instabilities. The ARIES design considered is a three field-period stellarator with engineering coil constraints optimized for magnetic well and alpha particle confinement. The reference design has high β ∼ 5%. The study is restricted to ideal modes and the calculations assume nested flux surfaces, with a limited plasma boundary surrounded by a vacuum. At β = 4%, with a conformal wall at twice the minor plasma radius, the equilibrium is slightly unstable to a periodicity-preserving, predominantly m/n = 9/6 mode peaked at the edge and a periodicity-breaking global m/n = 3/2 mode. At β ∼ 5%, these modes are destabilized but the growth rates are still moderate. At higher β, above the design value, several modes become unstable. Stabilization by a close fitting conducting wall is ineffective at β = 5% and below but becomes more effective at stabilizing external modes at higher β. The equilibrium at β ∼ 6% can be stabilized by a conformal wall at 1.1 times the minor plasma radius, although very weakly unstable internal modes remain at β > 6% with a wall on the plasma boundary. The sensitivity to the presence of the rational rotational transform ι = 2/3 surface at the edge of the plasma was also investigated. Generally, either the m/n = 3/2 mode is further destabilized or other modes are introduced. The stability calculations numerically impose a broadening of the singular perturbed current to eliminate spurious singularities. The effect of this is considered in detail and it is suggested that this numerical resonance detuning can model a physical broadening from non-ideal effects. Although the reference design with β ∼ 5% is above the strict ideal β limit, common experience in tokamaks indicates that weakly unstable internal modes and edge-localized modes result in relatively benign MHD activity. This is consistent with observations in large stellarator experiments that indicate some level of instability is tolerated and the results are discussed in this context and in relation to the numerical broadening of the singular perturbed currents.