We present a computational study of the internal optical forces arising in plasmonic gap antennas, dolmen structures and split rings. We find that very strong internal forces perpendicular to the propagation direction appear in these systems. These internal forces show a rich behaviour with varying wavelength, incident polarisation and geometrical parameters, which we explain in terms of the polarisation charges induced on the structures. Various interesting and anomalous features arise such as lateral force reversal, optical pulling force, and circular polarisation-induced forces and torques along directions symmetry-forbidden for orthogonal linear polarisations. Understanding these effects and mastering internal forces in plasmonic nanostructures will be instrumental in implementing new functionalities in these nanophotonic systems.