The linear magnetohydrodynamic stability of plasmas with sub‐Alfve´nic flows aligned parallel to the equilibrium magnetic field is treated. Subject to the constraints that the fluid is incompressible, inviscid, and perfectly conducting, it is demonstrated that stabilizing effects appear as the flow speed approaches the Alfve´n speed. The screw pinch plasma is treated explicitly, but it is conjectured that the conclusions are applicable to other equilibrium configurations.