The density shoulder at midplane may influence core plasma confinement during H-mode discharge, thus affecting long-pulse steady-state discharge. The drifts in the edge plasma plays remarkable role in the plasma transport and divertor operation regime, which determine the density shoulder formation (DSF). In this work, the SOLPS-ITER code package is used to evaluate the influence of full drifts on DSF in poloidal- and radial- coordinates. The open divertor of DIII-D like geometry with weak neutral compression is chosen for the modeling. Cases without drifts, with only E×B drifts in forward Bt, and with full drifts in both forward and reversed Bt are simulated for comparison. It is confirmed that the high upstream density promotes DSF when the drift is not considered, which has also been observed by various investigations. When the drifts are taken into account, the divertor in-out asymmetry (or upstream ionization source) is determined by the direction of Bt due to the variation of particle transport, thus the shoulder can be facilitated or suppressed. Two mechanisms of DSF with full drifts are elucidated: (1) the E×B and B×∇B drifts promote DSF at inner midplane (IMP) via raising ionization source (at IMP) in forward Bt; (2) the drifts contribute to DSF at outer midplane (OMP) by enhancing the radial transport in reversed Bt. In high recycling regime, the ionization is the dominant term for DSF, while in low recycling regime the enhanced radial transport by B×∇B drift plays more important role in DSF. Comprehensively understanding the DSF mechanisms is of great importance for the improvement of core-edge compatibility in the fusion reactor.