Nonlinear motion of magnetic vortices in soft magnetic squares is investigated by micromagnetic simulations, analytical calculations, and broadband ferromagnetic resonance measurements. Increasing amplitudes of alternating unidirectional spin currents and magnetic fields cause the shapes of the trajectories to approach the shape of the sample and shift the resonance frequency of vortex gyration. We show that it is the thickness of the magnetic element that determines whether the resonance frequency shifts to the red or to the blue. A nonlinear equation of motion based on the Thiele equation reproduces the simulated and measured results.