The flow at low Reynolds number around rectangular cylinders of varying chord-to-thickness ratios under transverse periodic forcing is studied numerically. Although of relatively low amplitude, the forcing locks the shedding from both the leading and trailing edges to the applied frequency. The base suction, and the lift and the drag on the cylinders are found to be complex functions of the forcing frequency. At low Reynolds numbers and without applied forcing, the flow is controlled by a global instability with the leading- and trailing-edge shedding locked; moreover, the reduced frequency of shedding varies in a stepwise manner with the chord-to-thickness ratio. This global instability is still evident in the flows under external forcing examined in this paper. While previous researchers have conjectured that the trailing-edge shedding plays a dominant role in the preferred frequency selection in the natural shedding case, the important role of trailing-edge shedding when the flow is forced is confirmed in the present study. In particular, the individual contributions from leading- and trailing-edge vortices on the perturbation to the leading-edge shear layer are examined. In addition, it is shown that the base suction is maximum when the forcing frequency is close to the global instability frequency observed in unforced flows, thereby strengthening the argument that the unforced, forced, and duct resonant cases are strongly influenced by the same global instability. The variations of the lift, drag and formation length with chord-to-thickness ratio are quantified.