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We use the concept of vectorial photochemical tweezing to rationalize the experimental observations of surface relief gratings in azo-polymers, e.g., the photochemically induced motion of the polymer in a one-dimensional intensity gradient produced by two-laser beam interference. Vectorial motion of matter occurs when photochemically active, polarization sensitive molecules are photo-selected in a gradient of light intensity. Directional motion is imposed parallel to the gradient vector with an efficiency that depends on the respective orientations of the vectors of light polarization and intensity gradient. Different combinations of polarizations of the interfering beams leading to differing efficiencies of matter motion are revisited and discussed. We show that the magnitude of photoisomerization force dictates the efficiency of the observed matter motion. We also show that the spatial distribution of the photo-moved matter is Gaussian, the height and width of which exhibit an intensity dependence which is predicted by the theory of photochemical vectorial tweezing; both theory and experiments indicate that the photoisomerization force, which acts on thin films of azo-polymers, is in the mN range.