We consider planarly oriented nematic liquid crystal subjected to plane, re
ctilinear, oscillatory Couette or Poiseuille flow in the case, when the dir
ector is initially perpendicular to the flow plane. Using the Galerkin meth
od we found the critical amplitude of the flow at which the homogeneous ins
tability develops. The analytical approximations for the frequency dependen
ce of the critical amplitude for different types of flow are obtained. The
results are compared with experimental data.