The growth rate of the resistive tearing mode is investigated in the presence of a sub‐Alfve´nic equilibrium plasma shear flow along the confining magnetic field and fluid viscosity. The flow exerts a destabilizing influence and the well‐known instability condition, &Dgr;’≳0, is modified to yield the possibility of instability with &Dgr;’≤0. The effects of viscosity on the marginal stability condition and the transition between the inviscid and viscous‐dominated limits are considered in detail.