This paper describes a Bayesian inversion of acoustic reflection loss versus angle measurements to estimate the compressional and shear wave velocities in young uppermost oceanic crust, Layer 2A. The data were obtained in an experiment on the thinly sedimented western flank of the Endeavor segment of the Juan de Fuca Ridge, using a towed horizontal hydrophone array and small explosive charges as sound sources. Measurements were made at three sites at increasing distance from the ridge spreading center to determine the effect of age of the crust on seismic velocities. The inversion used reflection loss data in a 1/3-octave band centered at 16 Hz. The compressional and shear wave velocities of the basalt were highly sensitive parameters in the inversion. The compressional wave velocity increased from 2547 + or - 30 to 2710 + or - 18 m/s over an age span of 1.4 million years (Ma) from the spreading center, an increase of 4.5 + or - 1.0%/Ma. The basalt shear wave velocity increased by nearly a factor of 2, from approximately 725 to 1320 m/s over the same age span. These results show a decreasing trend of Poisson's ratio with age, from a value of 0.46 at the youngest site closest to the ridge axis.