Shear wave splitting observed in microearthquake data at the axis of the Mid-Atlantic Ridge near 35¿N has a fast polarization direction that is parallel to the trend of the axial valley. The time delays between fast and slow S wave arrivals range from 35 to 180 ms, with an average of 90 ms, and show no relationship with ray path length, source-to-receiver azimuth, or receiver location. The anisotropy is attributed to a shallow distribution of vertical, fluid-filled cracks, aligned parallel to the trend of the axial valley. Joint modeling of the shear wave anisotropy and coincident P wave anisotropy results, using recent theoretical models for the elasticity of a porous medium with aligned cracks, suggests that the crack distribution that causes the observed P wave anisotropy can account for at most 10 ms of the shear wave delay. Most of the shear wave delay thus likely accrues within the shallowmost 500 m (seismic layer 2A), and the percent S wave anisotropy within this highly fissured layer is 8--30%. Isolated, fluid-filled cracks at 500 m to 3 km depth that are too thin or too shallow to be detected by the P wave experiment may also contribute to the shear wave delays. The joint analysis of P and S wave anisotropy is an important approach for constraining the crack distributions in the upper oceanic crust and is especially suited for seismically active hydrothermal systems at slow and intermediate spreading mid-ocean ridges.