The three-dimensional P and S wave structure of Redoubt Volcano, Alaska, and the underlying crust to depths of 7--8 km is determined from 6219 P wave and 4008 S wave first-arrival times recorded by a 30-station seismograph network deployed on and around the volcano. First-arrival times are calculated using a finite-difference technique, which allows for flexible parameterization of the slowness model and easy inclusion of topography and source-receiver geometry. The three-dimensional P wave velocity structure and hypocenters are determined simultaneously, while the three-dimensional S wave velocity model is determined using the relocated seismicity and an initial S wave velocity model derived from the P wave velocity model assuming an average Vp/Vs ratio of 1.78. Convergence is steady with approximately 73% and 52% reduction in P and S wave arrival time RMS, respectively, after 10 iterations. The most prominent feature observed in the three-dimensional velocity models derived for both P and S waves is a relative low-velocity, near-vertical, pipelike structure approximately 1 km in diameter that extends from 1 to 6 km beneath sea level. This feature aligns axially with the bulk of seismicity and is interpreted as a highly fractured and altered zone encompassing a magma conduit. The velocity structure beneath the north flank of the volcano between depths of 1 and 6 km is characterized by large lateral velocity variations. High velocities within this region are interpreted as remnant dikes and sills and low velocities as regions along which magma migrates. No large low-velocity body suggestive of a magma chamber is resolved in the upper 7--8 km of the crust. ¿ American Geophysical Union 1996