  We study the effect of a uniform shear flow on an interface separating the
two broken-symmetry ordered phases of a two-dimensional system with
nonconserved scalar order parameter. The interface, initially flat and
perpendicular to the flow, is distorted by the shear flow. We show that there
is a critical shear rate, \gamma_c, proportional to 1/L^2, (where L is the
system width perpendicular to the flow) below which the interface can sustain
the shear. In this regime the countermotion of the interface under its
curvature balances the shear flow, and the stretched interface stabilizes into
a time-independent shape whose form we determine analytically. For \gamma >
\gamma_c, the interface acquires a non-zero velocity, whose profile is shown to
reach a time-independent limit which we determine exactly. The analytical
results are checked by numerical integration of the equations of motion.
