Measurements of compressional wave attenuation are presented for 30 low porosity (phi = 0.4 - 8.8%) oceanic basalts collected from 10 ODP and DSDP drill sites. Additionally, the first laboratory measurements of shear wave attenuation in oceanic basalt are presented for 14 rocks from the test suite. Experiments were conducted on saturated samples under elevated confining pressures. Attenuation coefficients (alpha ) range from 2.48 dB/cm to 9.99 dB/cm for shear propagation and 0.32 dB/cm to 4.69 dB/cm for compressional propagation at 150 MPa. P and S wave quality factors (Q) were calculated from measured group velocity and attenuation coefficient data. Q (sub p) and Q (sub s) values range from 14.0 to 166.8 and 8.0 to 27.2, respectively. Both Q and alpha show a significant pressure dependence when subjected to confining pressures up to 400 MPa. This pressure dependency is caused by the opening and closing of compliant microcracks. Q and alpha , both shear and compressional, are also shown to depend on porosity with alpha increasing and Q decreasing with porosity. No significant relationship is found between attenuation and age or in situ depth for samples from drill Sites 417, 418, 483, or 485, while samples from Hole 504B show a significant decrease in attenuation with depth below sea floor. Qs/Qp ratios are determined for 14 samples from the test suite and prove to be good indicators for degree of saturation when combined with Vp/Vs ratio data. Qs/Qp ratios vary from 0.12 to 0.40 for saturated samples and 0.37 to 1.06 for two oven dry basalt samples. Dry samples generally display high Qs/Qp ratios (>0.4) and low Vp/Vs ratios (<1.75), while the inverse is true for saturated samples (Qs/Qp<0.4 and Vp/Vs>1.75). Mechanisms most likely responsible for the observed high P and S wave attenuation are grain boundary frictional sliding, and viscous local or "squirt" flow. Data presented are in good agreement with previous studies of attenuation mechanisms in sandstone and carbonate. Laboratory data is also comparable to field seismic measurements of oceanic Layer 2A Qp; however, there is no clear explanation for this agreement, since no attenuation mechanism has been proven to dominate at both high (MHz) and low (Hz) frequencies. One possible explanation given is the presence of a viscous fluid flow mechanism at both frequency scales.