Abstract Large-amplitude (geometrically nonlinear) vibrations of circular cylindrical panels with rectangular base, simply supported at the four edges and subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated. Two different nonlinear strain–displacement relationships, from the Donnell's and Novozhilov's shell theories, are used to calculate the elastic strain energy. In-plane inertia and geometric imperfections are taken into account. The solution is obtained by Lagrangian approach. The nonlinear equations of motion are studied by using (i) a code based on arclength continuation method that allows bifurcation analysis and (ii) direct time integration. Numerical results are compared to those available in the literature and convergence of the solution is shown. Interaction of modes having integer ratio among their natural frequencies, giving rise to internal resonances, is also discussed.