The dynamic response of an atomic force microscope cantilever probe is studied for off-resonance excitation and interactions with a soft silicone rubber material. The dynamic response of the probe is simulated using a three-mode approximation of the Euler-Bernoulli beam model for excitation at two-and-a-half times the probe’s fundamental frequency. These simulations are conducted in order to reproduce the period-doubling bifurcation experimentally observed in the response of the probe of a commercial atomic force microscope. In order to duplicate this behavior, parameters within the surface force model are tuned to account for variations in the characteristics of the sample material. Through this work, the relationship between the sample material’s effective stiffness and the response behavior of the probe are studied in an effort to develop the means to identify the local material properties of a sample by characterize the nonlinear response of the probe.