We study the vibrational motion of mechanical resonators under strong drive in the strongly nonlinear regime. By imaging the vibrational state of rectangular silicon nitride membrane resonators and by analyzing the frequency response using optical interferometry, we show that, upon increasing the driving strength, the membrane adopts a peculiar deflection pattern formed by concentric rings superimposed onto the drum head shape of the fundamental mode. Such a circular symmetry cannot be described as a superposition of a small number of excited linear eigenmodes. Furthermore, different parts of the membrane vibrate at different multiples of the drive frequency, an observation that we denominate as "localization of overtones." We introduce a phenomenological model that is based on the coupling of a small number of effective nonlinear resonators, representing the different parts of the membrane, and that describes the experimental observations correctly.