The Puget Sound region of Western Washington is represented by nearly cubic blocks of 5 km per side. P-wave arrival time observations from 4387 crustal earthquakes, with depths of 0 to 40 km, were used as sources producing 36 865 rays covering the target region. A conjugate gradient method (LSQR) is used to invert the large, sparse system of equations. To diminish the effects of noisy data, the Laplacian is constrained to be zero within horizontal layers. The resolution is estimated by calculating impulse responses at blocks of interest and estimates of standard errors are calculated by the jackknife statistical procedure. Results of the inversion are correlated with some known geologic features and independent geophysical measurements. High P-wave velocities along the eastern flank of the Olympic Peninsula are interpreted to reflect the subsurface extension of Crescent terrane. Low velocities beneath the Puget Sound further to the east are inferred to reflect thick sediment accumulations. The Crescent terrane appears to extend beneath Puget Sound, consistent with its interpretation as a major accretionary unit. In the southern Puget Sound basin, high velocity anomalies at depths of 10-20 km are interpreted as Crescent terrane and are correlated with a region of low seismicity. Near Mt. Rainier, high velocity anomalies may reflect buried plutons