Here we report the theory formulation and the experiment realization of sum-frequency generation vibrational spectroscopy （SFG-VS） in the cross-propagation （XP） geometry or configuration. In the XP-SFG-VS, the visible and the infrared （IR） beams in the SFG experiment are delivered to the same location on the surface from visible and IR incident planes perpendicular to each other, avoiding the requirement to have windows or optics to be transparent to both the visible and IR frequencies. Therefore, the XP geometry is applicable to study surfaces in the enclosed vacuum or high pressure chambers with far infrared （FIR） frequencies that can directly access the metal oxide and other lower frequency surface modes, with much broader selection of visible and IR transparent window materials. The potential applications include surface science, material science, fundamental catalytic sciences, as well as low temperature molecular sciences, etc.
