The 3D moldability of veneers, as opposed to the moldability of plastic or other materials, is limited because of the characteristics of wood. By mechanical treatment under appropriate conditions, it is possible to partially modify veneer characteristics. In this study, the intention was to determine the effect of factors influencing the 3D moldability of veneers. Therefore, this study was focused on determining the 3D moldability of veneers with square and circular shape, which were stressed under six moisture content levels (i.e., 0%, 8%, 16%, 20%, 30%, and 100%). To determine the influence of wood species, the results for beech veneers of 0.5-mm thickness were compared to the results for birch veneers of 0.5-mm thickness. These sets of samples were stressed with a spherical stamping tool with three different radii of curvature (i.e., 20, 40, and 80 mm). There is currently no standardized method for assessing the 3D moldability of veneers, as opposed to metals (metal sheets). Because of the low moldability of veneers compared to metal materials, Erichsen's method for assessing the moldability of metal sheets was modified for veneers. The 3D moldability was determined based on maximal deflection of the veneer stressed by the stamping tool before rupture. Based on the established method, the effects of wood species, moisture content of veneers, diameter of stamping tool, and shape of samples on deflection during 3D molding were determined.