In the laboratory, rocks display highly elastically nonlinear behavior. Characteristic parameters of nonlinear elasticity can be measured in a resonant bar experiment. Two important features of nonlinear resonant behavior are a shift in resonant frequency away from the linear resonant frequency as the amplitude of the disturbance is increased, and the harmonics in the time signal that accompany this shift. We have conducted Young's mode resonance experiments using bars of a variety of rock types (limestone, sandstone, marble, chalk) and of varying diameters and lengths. Typically, resonant frequency shifts of 10% or more are observed at strains of 10-7 - 10-6 for samples at a variety of saturation conditions and ambient pressure conditions. Correspondingly rich spectra measured from the time signal progressively develop with increasing drive level. To date, the resonant peak is observed to always shift downward (if indeed the peak shifts), indicating a net softening of the modulus with drive level. This observation is in agreement with our pulse-mode and static test observations, and those of other researchers. Resonant peak shift is not always observed even at large drive levels. This is an unexpected result; however, harmonics are always observed even in the absence of peak shift when detected strain levels exceed 10-7 or so. Important implications for measurement of modulus and Q (inverse attenuation) also result from our study. Resonant peak shift may begin at even the lowest drive levels in rock when it occurs, and peak shift and peak width is dependent on frequency sweep direction. Therefore, measurement of moduli and Q must be undertaken with great caution. Ultimately, we hope to apply this technique to characterizing the nonlinear response of rock, to study of progressive change in material property, to applications in nondestructive evaluation, and to understanding of the nonlinear response of the earth's crust.