The crystal structures of Nb3Te4 and InxNb3Te4 [x = 0.539 (4)] are reported for a series of pressures between 0 and 40 GPa. Both compounds crystallize in space group P6(3)/m with a = b = 10.671 and c = 3.6468 A for Nb3Te4, and a = b = 10.677 and c = 3.6566 A for InxNb3Te4 at ambient conditions. Phase transitions were not observed. High-pressure X-ray powder diffraction was measured using a diamond anvil cell and synchrotron radiation. Full Rietveld refinements provided the values of the lattice parameters and the values of the atomic coordinates at each pressure. The bulk modulus is found as K(0) = 70 (5) GPa for Nb3Te4 and as K(0) = 73 (4) GPa for InxNb3Te4. The analysis of the pressure dependences of the detailed crystal structures shows that the compression along c involves the folding up of the quasi-one-dimensional zigzag chains of Nb. The compression perpendicular to c is entirely due to the reduction of the diameter of the channels. The presence of intercalated In atoms is found to have hardly any influence on the compression behaviour up to 40 GPa.