Low temperatre X-ray diffraction analysis of Nb
3Sn multifilamentary wires produced by the bronze route has been performed at different orientations. An important volume fraction of the Nb
3Sn filaments is found to undergo a stress-induced cubic-tetragonal transformation with

at 10 K. Strong texturing of the tetragonal phase has been detected: the shorter c axis is preferentially oriented along the wire axis. The present data furnish a direct indication for the uniaxial stress distribution in the wire. Careful H
c2(T) measurements on a wire at the vicinity of T
creveal a sharp change of the slope dH
c2/dT|T
c. This is interpreted as a physical proof for the coexistence of two phases at low temperature, with T
c(cub.) < T
c(tetr.), but H
c2(cub.) > H
c2(tetr.). Based on these data, the variation of the ratio J
cm/J
coof Nb
3Sn multifilamentary wires under uniaxial stress can be correlated with the presence of the tetragonal phase. The applied strain is believed to affect as well the the tetragonal volume fraction as the ratio c/a of the tetragonal phase.