An explanation is given for the mechanical resonance dispersions observed at audio‐frequencies in many crystalline solids. The resonances are considered to result from alternating simultaneous slip occurring on transient slip planes with mean lifetimes of 10−2 to 10−4 sec. The slip along such planes is opposed by displacement‐dependent, velocity dependent, and acceleration‐dependent stresses. These last two stresses are found to be of magnitudes which can result from the interchange of atoms across a slip plane with a consequent decrease of momentum of the fast moving (slipped) part of the sample undergoing deformation. If the rate of transfer is independent of the slip process, a velocity‐dependent (viscous) stress results, but if some of the atoms are induced to transfer as a direct result of the slip itself, then an acceleration‐dependent stress is present. These slip planes, because of their sudden formation, short lifetimes, and inertial coefficients, do not contribute to the static or ultrasonic compliance, but do affect the dynamic compliance at audio frequencies. The transient slip planes are supposed to be generated by the movement of dislocations across the sample. Thus, a concept of combined consecutive and simultaneous slip is suggested in which dislocations remain an essential part of the mechanism but are not the sole source of deformation. An interesting consequence of the theory is that a critical stress for plastic flow or, alternatively, for brittlefracture can be predicted from values of the dynamic compliance (or modulus). Predicted values of critical stress (for both single crystals and polycrystalline metals) made from the dynamic modulus at 100 cps are much closer to the observed values than those made on the basis of either the static or ultrasonic moduli. In particular, it is found that the predicted values for brittlefracture stress agree almost exactly with observed breaking stresses for single crystals of sodium chloride, germanium, glycine sulfate, and, at two temperatures and orientations, for natural quartz crystals. The occurrence of negative absorption or induced emission is discussed, and a means of generating sustained, self‐excited, audio‐frequency oscillations in a crystalline solid is outlined. The possibility of mechanical failure at an intrinsic material resonance is considered briefly and some other aspects of the mechanical behavior of crystalline solids are also examined.