We present the results of our theoretical studies on the repulsive (pushing) manipulation of a C₆₀ molecule on the Si(001) surface with several scanning tunnelling microscopy tips. We show that, for silicon tips, tip–C₆₀ bonds are formed even with tips that do not initially have dangling bonds, and this tip–C₆₀ interaction drives the manipulation of the molecule. The details of the atomic structure of the tip and its position relative to the molecule do not have a significant effect on the mechanism and the sequence of adsorption configurations during the pushing manipulation of C₆₀ along the trough, where the trough itself provides a guiding effect. The pushing manipulation is thus a very robust process that occurs largely independently of the tip structure. On the other hand, the pushing manipulation across an Si–Si dimer row into the neighbouring trough proceeds in a more complex way, with tip deformation and detachment more likely to occur. We demonstrate the role of tip deformation and tip–molecule bond rearrangement in the continuous manipulation of the molecule. Finally, we calculate and analyse the forces acting on the tip during manipulation and identify characteristic patterns.