We develop new 3D full vectorial finite element bidirectional beam propagation method (3DFV-BiBPM) in order to handle the nonradiative dielectric waveguide (NRD guide) components where waveguide profile varies in the direction perpendicular to the parallel metal plates. The BiBPM is one of the transfer-matrix-based methods where only transverse cross sections have to be discretized using the finite difference or the finite element scheme, and it can treat backward and multiple reflections as opposed to the standard BPM. An NRD guide with air-gap and a filter with a sapphire resonator are numerically analyze considering dielectric losses to investigate the validity of our approach.