Two samples with the compositions Ti3PD0.42 and Ti3PD0.67 have been prepared and studied by diffraction methods in order to determine the crystal structures; in particular, the location of the deuterium atoms. Neutron powder diffraction data were collected at the R2 reactor in Studsvik, Sweden, and analysed with the Rietveld method. The final agreement factors obtained after the profile refinements were R(I) = 0.056, R(p) = 0.034 and R(wp) = 0.043 for Ti3PD0.42 and R(I) = 0.057, R(p) = 0.033 and R(wp) = 0.042 for Ti3PD0.67. The crystal structure of Ti3P is tetragonal, space group P4(2)/n (No. 86), with unit cell dimensions a = 9.9640(5) angstrom, c = 4.9887(4) angstrom and Z = 8. The Ti-P host lattice remains essentially unchanged, except for some moderate expansion, upon deuterium absorption within the concentration range investigated in this study. The unit cell volume expansions are 1.2% and 1.9%, respectively. Two different kinds of tetrahedral Ti4 interstices were found to accommodate the deuterium atoms. The shortest D-D, D-Ti and D-P distances were calculated to be 1.92, 1.82 and 2.61 angstrom, respectively.