A simple new technique predicts the high- and low-frequency saturated velocities in anisotropic rocks entirely in terms of measurable dry rock properties without the need for idealized crack geometries. Measurements of dry velocity versus pressure and porosity versus pressure contain all of the necessary information for predicting the frequency-dependent effects of fluid saturation. Furthermore, these measurements automatically incorporate all pore interaction, so there is no limitation to low crack density. The velocities are found to depend on five key interrelated variables: frequency, the distribution of compliant crack-like porosity, the intrinsic or noncrack anisotropy, fluid viscosity and compressibility, and effective pressure. The sensitivity of velocities to saturation is generally greater at high frequencies than low frequencies. The magnitude of the differences from dry to saturated and from low frequency to high frequency is determined by the compliant or crack-like porosity. Predictions of saturated velocities based on dry data for sandstone and granite show that compressional velocities generally increase with saturation and with frequency. However, the degree of compressional wave anisotropy may either increase or decrease upon saturation depending on the crack distribution, the effective pressure, and the frequency at which the measurements are made. Shear-wave velocities can either increase or decrease with saturation, and the degree of anisotropy depends on the microstructure, pressure, and frequency. Consequently great care must be taken when interpreting observed velocity anisotropy for measurements at low frequencies, typical of in situ observations, will generally be different from those at high frequencies, typical of the laboratory.