We demonstrate that mechanical hysteresis loop shapes for a linear anelastic solid satisfying Q-1? constant over a wide frequency range are sensitive to the cycling stress waveform. Cusped or asymmetrical hysteresis loops are compatible with linear anelastic behavior for nonsinusoidal loading and do not necessarily imply a nonlinear attenuation mechanism. Because loop shape depends on the cycling stress waveform, we suggest that detailed observation of the stress time function, the hysteresis loop shapes, and experimental determination of the creep function over a time interval comparable to that of the cyclic loading experiment provide a direct and stringent test of the linearity of rock attenuation. Such detailed observation of hysteresis loop shapes during nonsinusoidal stress cycles can also provide a test in the linear range for theoretically constructed creep functions.