We have determined the three-dimensional P wave velocity structure and azimuthal anisotropy within the shallow crust of the inner valley at the Mid-Atlantic Ridge (MAR) near 35 ¿N. The best fitting one-dimensional model is ~0.8 km/s lower in velocity at a given depth than for fast spreading ridges, while the isotropic three-dimensional velocity structure shows a strong lateral heterogeneity (up to 1.4 km/s peak-to-peak variation at 1 km depth) in both the along- and cross-axis directions. An anomalous region, with velocities as much as 0.8 km/s lower than average and 3--5 km in lateral extent, is located beneath a near-axis seamount. We interpret this feature as a region of near-solidus temperatures with possibly a small degree of partial melt. From the variation of travel time residuals with azimuth we determine a best fitting P wave anisotropy model that has 4% anisotropy from 500 m to 1 km depth, 2% anisotropy in the depth range 1--1.5 km, and no anisotropy at greater depth. This finding is consistent with vertical cracks aligned parallel to the axial valley. We find no evidence for the shallow, high-velocity, ridge-parallel feature commonly observed at the axis of fast spreading ridges and attributed to high-velocity dikes beneath a thin extrusive layer. The absence of this anomaly at the MAR implies that the axis of crustal accretion is not at a stable location with respect to the inner valley walls on timescales greater than about 25,000 years. An unstable axis of accretion will result in a thicker transition from extrusive rocks to dikes, which may account for the generally lower velocities beneath the MAR compared with the East Pacific Rise, and a lateral variation in upper crustal lithology. ¿ 1998 American Geophysical Union