The problem of short harmonic capillary waves propagation with small amplitude at the nematic-isotropic interface with Rapini-Papoular model for surface tension is considered. The case of Frank-Oseen approximation is studied then viscosity is isotropic, and equations for director and velocity are independent and they are related due to the anisotropic surface tension. For this model the problem of surface waves propagation is solved. The dispersion relation is deduced and studied. Also the stability of this wave is analyzed. It is shown that stability is depended from the divergent member coefficient in the Frank-Oseen free energy expression.