The crystal structure of the quasi-one-dimensional cuprate Sr2CuO3 has been studied under high pressure using neutron powder diffraction methods. Full structure refinements were undertaken, using the Rietveld method, with data acquired between room pressure and 0.55(1) GPa at room temperature. The compressibility of Sr2CuO3 is anisotropic, a consequence of the ordered nature of the anion vacancies in this material. The effect of high pressure and chemical substitution on the crystal structure of the Sr2-xCaxCuO3 system is discussed and it is suggested that the substitution of Sr2+ by Ca2+ may constitute a "chemical pressure" effect in this solid solution. The availability of accurate bond length compressibility data for Sr2CuO3 may now allow an appraisal of the effect of applied pressure on the remarkable electronic properties of this material, through appropriate band structure calculations.