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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 …