The intensive use of flexographic printing for packaging decoration and the increased consumer demands for it require an in-depth study of the factors that influence the prints’ quality. In this paper, we examined the test prints obtained at a flexographic proofer. Images on cardboard were printed by the environmentally friendly inks made by a Ukrainian manufacturer. The effect of the cardboard surface layer on the microgeometry of the prints created by cyan, yellow, black, and magenta inks has been shown. It has been established that the roughness parameter Ra for a two-layer coated cardboard is reduced by 3 times as compared to the uncoated cardboard. The photographs of the microstructure of the prints’ surface, their profile demonstrate a significant effect of the chalked coating on the image quality. It has been confirmed that the ink layer smooths out the micro-roughness of the print surface. However, when printed on the uncoated cardboard, the ink particles penetrate deeper into the structure and do not completely smooth out its micro-roughness. If the size of the printing element is smaller than the size of the cell on a raster roller, it falls into this cell and the ink is applied beyond the boundaries of the image. As a result, a spot of an arbitrary shape is formed on the print instead of a raster dot of a certain size, that is, the so-called "inverse tone transfer" occurs. We have measured the densitometric indicators of prints (optical density, gray balance), which significantly affect the quality of the product. Based on a Harrington's desirability function, the maximum permissible values of optical density, evenness of printing, contrast, dot gain of raster elements, and trapping, have been calculated. According to the generalized optimization criterion, a comprehensive index of the prints’ quality has been determined, which could ensure the predicted quality of a would-be run of the printed products, and would make it possible to adjust the printing process if necessary