The coupled rib waveguieds are analyzed by using Galerkin method based on the plane mapped boundary conditions. The results indicate that the coupling ability decreases with increasing of the rib height and attenuates exponentially with increasing of the waveguides separation. The field intensity distributions of the even and odd modes supported by the coupled rib optical waveguides are obtained. Comparatively agreeing with those previously published, the results can be used to optimize the structural parameters for photonic devices. In addition, the plane mapped boundary conditions eliminate the non-physical reflection, and the small matrix derived from this method promotes the computational efficiency.