  We have investigated surface acoustic wave propagation in Ni/LiNbO$_3$ hybrid
devices. We have found the absorption and phase velocity are dependent on the
sign of wave vector in a device, which indicates the nonreciprocal propagation
characteristic of systems with time reversal and spatial inversion
simultaneously broken symmetries. The nonreciprocity is reversed by the
180$^\circ$ rotation of magnetic field. Nonreciprocity seems largely dependent
on the shape of ferromagnetic Ni film. The origin of these observations is
ascribed to film shape dependent magnetoelastic coupling.
