The texture of two depleted uranium (DU) samples, labelled DUWR and DUWR2, were studied by neutron diffraction. DUWR was prepared by warm rolling of a cast ingot, and DUWR2 was prepared by adding 20% tensile strain to the warm-rolled DUWR. Complete three-dimensional orientation distribution functions were determined using four neutron pole figures for the DUWR, and using six neutron pole figures for the DUWR2 sample, by the WIMV method of the program popLA. The textures of the two samples were essentially identical to each other. They could be described by a twisted helical density tube spiralling continuously along the psi-axis of the Euler space. The projection of the backbone of the density tube along the theta-axis cast a linear shadow running parallel to the diagonal of the phi-psi plane, which could be defined by a phi = psi + 90 degrees (and phi = psi + 270 degrees) relation. The helical tube was confined with in narrow theta-angle limits, from 14 degrees to 30 degrees with the peak orientation at (103) [010]. The diffraction patterns of the DUWR2 sample were measured from the normal direction to the rolling surface of the sample, up to the scattering angle of 108 degrees using a 0.15 nm neutron beam. The Rietveld profile refinement using the textured diffraction pattern was quite satisfactory when the texture effect to the entire diffraction profile was corrected for by the corresponding pole density from the inverse pole figure.