The measured attenuation (Q-1) of a rock is a function of a number of parameters, one of those being the applied strain amplitude. It is important to understand the effect that strain amplitude has on Q-1 for several reasons: different measurement techniques use differing strain amplitudes and may measure a dissimilar Q-1, near source (large strain) wave propagation may behave highly non-linearly, and the strain amplitude dependence can provide insight into the attenuation mechanism. A physical model based on the contact friction between crack surfaces in the rock has been developed to describe rock deformation and dissipation under large applied strain. The three-dimensional crack surfaces are characterized by a statistical distribution of asperity heights. The sliding contact of these spherically-tipped asperities dissipates frictional energy. Hertzian theory is applied to the average asperity contact and predicts that the large strain attenuation is given by Q-1=k&zgr;&Egr;/P4/3, where k is a constant consisting of the matrix elastic parameters, &zgr; is the crack density, &Egr; is the strain amplitude, and P is the confining pressure. The total attenuation measured appears to be the sum of this strain dependent term and a strain independent term. The results of ultrasonic pulse transmission experiments are compared with the model's prediction. Both P and S waves with strain amplitudes from 10-8 to 10-5 were employed. Frequencies from 0.4 to 1.5 MHz were used in conjunction with rock confining pressures of 2 to 580 bars on dry Berea sandstone and lucite samples. The spectral ratio method and rise time technique were applied to deduce the Q-1 values. The observed data and other observations from the literature compare well with the model's prediction for the dependence of Q-1 on large strain amplitude, crack density, and pressure.