This paper presents the free vibration of thin doubly-curved shallow shells of rectangular planform. The study covers wide combinations of free, simply supported and clamped boundary conditions. Both positive and negative Gaussian curvatures (spherical and hyperbolic paraboloidal shells resepectively) are considered. The pb-2 Ritz energy based approach, along with the in-plane and transverse deflections assumed in the form of a product of mathematically complete two-dimensional orthogonal polynomials and a basic function, is employed to model the vibratory characteristic of these shells. Numerical results have been established through convergence study and comparison with published data from the open literature. Extensive sets of new results for various ranges of aspect ratio, curvature ratio and x- and y- shallowness ratios have been presented for future reference.