Recordings of 281 small earthquakes which occurred recently near the southern edge of Long Valley caldera at depths from1 to 15 km are used to map the subsurface geometry of shear wave attenuating bodies in the caldera. Signatures of these events recorded northwest, north, northeast, and east of Long Valley with ray paths through the caldera are often anomalous in that S wave arrivals have very low amplitudes and high frequency P and S wave enegy is missing for the same station-event combinations. The volcanic and geothermal history of the region suggests that ray paths for these anomalous signals have passed through magma which absorbed much of the S wave energy and also attenuated the higher frequencies. With over 1200 normal and anomalous ray paths through the caldera we have located two apparently massive magma bodies in the central and northwest caldera as well as two more dispersed magma areas in the southern caldera and beneath Crowley Lake. The central magma body extends from 4.5 to at least 13 km beneath the surface, and the northwest body is a shallow as 5.5 km. These two magma bodies are probably connected below about 8 km. Secondary arrivals seen on select seismograms are tentatively interpreted as reverberations inside the central magma chamber and are consistent with the interpreted lateral extent of the magma. The northwest and center magma bodies lie beneath and southeast corners of the caldera's resurgent dome and probably connect beneath the dome's center. Also the shallower parts of these magma bodies and the southern anomalous area lie beneath the surface expression of the medial graben faults suggesting that structural features seen at the surface of the valley may be related to magma location at depth.