Vectorial eigenmodes supported by the buried rectangular and rib optical waveguides are obtained using variable transformed series expansion method. The infinite x-y plane is mapped into a unit square by an elegant tangent-type variable transformation. Consequently, the boundary truncation is not necessary, and the nonphysical reflection is eliminated. As a result, the calculation accuracy is promoted. In addition, small matrix derived from this method promotes the computational efficiency. Comparatively agreeing with those previously published, the results can be used to optimize the photonic devices.