Abstract Part II of this series of four papers deals with the free vibration analysis of thick rectangular plates with internal oblique line supports. An energy functional is derived based on Mindlin's plate theory, and this is minimized using the pb-2 Rayleigh-Ritz method, leading to the governing eigenvalue equation. In the process of minimization, sets of mathematically complete two-dimensional polynomials are assumed in the displacement and rotation functions to approximate the appropriate mode shapes. Rectangular plates supported by various types of internal line support are considered, and this paper includes sets of reasonably accurate vibration frequencies for these plates. Results are presented for a wide range of aspect ratios a b and relative thickness ratios t b . For completeness, 21 distinct combinations of boundary conditions have been considered. The results may serve as design data for engineers and designers in the practical application of plate vibration analysis.