The ideal stability of cylindrical plasma with mass flows is investigated using the guiding center plasma (GCP) model of Grad [ProceedingsoftheSymposiumonElectromagneticandFluidDynamicsofGaseousPlasmas(Polytechnic Inst. of Brooklyn, New York, 1961), p. 37]. For rotating plasmas, the kinetic treatment of the parallel motion in GCP gives significantly different results from the fluid models, where the pressures are obtained from equations of state. In particular, GCP removes the resonance with slow magnetoacoustic waves and the loss of stability that occurs in magnetohydrodynamics (MHD) for near‐sonic flows. Because of the strong kinetic damping of the sound waves in an isothermal plasma, the slow waves have little influence on plasma stability in GCP at low beta. In the large aspect ratio, low‐beta tokamak ordering, Alfve´nic flows are needed to change the ideal GCP stability significantly. At lowest order in the inverse aspect ratio, flow can be favorable or unfavorable for stability of local modes depending on the profiles, but external kinks are always destabilized by flow if the velocity vanishes at the edge. For high‐beta, reversed field pinch equilibria, numerical computations show that flow can be stabilizing for local modes, but external modes are destabilized by flow. In three dimensions, the MHD equilibrium problem becomes hyperbolic for arbitrarily small flows across the magnetic field, whereas the GCP equilibrium equation remains elliptic for sub‐Alfve´nic flows.