Bifurcations are studied for off-resonance excitation in atomic force microscopy (AFM). The position and type of the bifurcation is determined to be dependent upon the effective modulus of the sample and the stiffness of the AFM probe. The current effort consists of a parametric study by using numerical integration and numerical continuation methods. The influence of the sample material modulus on the characteristic of the bifurcation is studied as a potential means to perform localized nano-scale material characterization.