Solid elements are increasingly utilized in finite element analysis of sheet metal stamping processes with the rising application of advanced high strength steels (AHSSs) and aluminum alloys in auto industries as these advanced materials fail in a form of rupture with negligible necking during sheet metal stamping. However, there are rare orthotropic yield functions for the description of directional dependence of plastic deformation of body-centered cubic (BCC) materials and face-centered cubic (FCC) metals under spatial loading, especially for metals with moderate anisotropy. For this purpose, the Yld2004-18p function is revisited and modified to provide satisfactory predictability of orthotropic behavior of BCC and FCC materials under spatial loading with reduced experimental costs for the calibration of orthotropic coefficients. The reduced Yld2004 equation is utilized to characterize the directional dependence of plastic behavior of AHSSs and aluminum alloys to verify its promising accuracy and cost efficiency. The reduced Yld2004 function is also implemented into finite element analysis to assess its accuracy and computation efficiency compared with the Hill48, Yld2004-18p and the anisotropic Drucker equations. The application in both analytical prediction and numerical analysis proves that the reduced Yld2004 function provides competitive predictability of anisotropic plastic deformation for BCC and FCC metals with moderate directionality under triaxial stress states, but the cost for the parameter calibration is cut down by about half compared to the Yld2004-18p function. Considering the satisfactory accuracy, reduced cost for the parameter calibration as well as the fact that most metals are of gentle dependence on loading direction, the reduced Yld2004 function is expected to reliably reproduce actual stamping processes of the majority of AHSSs and aluminum alloys with virtual models thereby improving the credibility of both numerical design of tools and process optimization.