This paper presents the first known analytical solution for vibrations of a polarly orthotropic Mindlin sectorial plate with simply supported radial edges. The solution is a series solution constructed using the Frobenius method and exactly satisfies not only the boundary conditions along the radial and circular edges, but also the regularity conditions at the vertex of the radial edges. The moment and shear force singularities at the vertex are exactly considered in the solution. The correctness of the proposed solution is confirmed by comparing non-dimensional frequencies of isotropic plates obtained from the present solution with published data obtained from a closed-form solution. This paper also investigates the effects of elastic and shear moduli on the vibration frequencies of the sectorial plates with free or fix boundary conditions along the circumferential edge. A study is also carried out about the influence of elastic and shear moduli on the moment and shear force singularities at the plate origin (r = 0) for different vertex angles.