The influence of shear plasma flow along the magnetic field on the resistive tearing instability has been investigated in plane geometry. It is shown that such flows, even at significantly sub‐Alfve´nic speeds, have a destabilizing effect. Moreover, in nonsymmetric cases, the well‐known threshold for tearing mode instability &Dgr;′ext=0 is removed. Thus, in magnetic configurations which would otherwise be stable in the absence of flow, a shear plasma flow can induce instability. Approximate growth rates have been obtained for tokamaks with significant equilibrium plasma rotation and an application to the ISX‐B experiments is briefly discussed.