Large-amplitude vibrations of circular cylindrical panels (open shells) subjected to harmonic excitation are numerically and experimentally investigated. The Donnell nonlinear strain-displacement relationships are used to describe the geometric nonlinearity; in-plane inertia is taken into account. Specific boundary conditions, with zero transverse displacement at the panel edges and free or elastically restrained in-plane displacements, not previously considered, have been introduced in order to model the experimental boundary conditions. The nonlinear equations of motion are obtained by the Lagrange equations with multi-mode approach, and are studied by using a code based on the pseudo-arclength continuation method. Two thin circular cylindrical panels of different dimensions and made of stainless steel have been experimentally tested in the laboratory for several excitation amplitudes in order to characterize the nonlinearity. The dimensions of the two panels have been chosen in order to have the fundamental mode with one and two circumferential half-waves, respectively. Numerical results are able to reproduce the experimental results with high accuracy for both panels. The effect of geometric imperfections on the trend of nonlinearity and on natural frequencies is shown; convergence of the solution with the number of generalized coordinates is numerically verified.