Derived from the eigenvector method (EM), a vectorial eigenvector method (VEM) for the mode calculation of polarization dependent resonator is presented. New transfer matrices of laser resonant cavities with polarization-selective devices are built by using Jones matrix representation. The eigenvectors computed by solving the matrix eigenequation manifest the mode characteristics of resonators, including cylindrical vector (CV) modes. Comparing with EM, the VEM inherits EM's superiorities and extends scalar models to vector models. Then, an example utilizing VEM to simulate axicon mirror resonator was given, which proved the VEM feasible and efficacious. Finally, upon a fast axial flow (FAT) CO2 laser with an axicon mirror as rear mirror, we experimentally corroborated the validity of the VEM and a working-stable 1.5 kW radially polarized beam was obtained.