The use of mechanically-fastened fibre-reinforced polymer (MF-FRP) strips has been recently proposed as a possible alternative solution to the most common externally-bonded (EB) sheets and laminates. Although several applications of MF-FRP strengthening on reinforced concrete (RC) structures are already available, further experimental and theoretical studies are needed for both achieving a thorough knowledge of their mechanical behaviour and formulating sound design rules. The present paper deals with identifying the relationships between the actual bearing stress transferred by the fastener and the corresponding relative displacement (slip) at the FRP–concrete interface. For this purpose, a simplified numerical model is firstly formulated to simulate the experimental behaviour observed from direct shear tests (DSTs) recently performed by the Authors on FRP laminates fastened to concrete blocks with screwed steel anchors. Then, the numerical model is employed within an optimisation procedure aimed at indirectly identifying the relationships between the force applied on the single fastener and the corresponding displacement. Finally, the results of this inverse identification procedure are compared for pointing out the differences possibly arising in terms of interface stress–slip relationship as a result of different detailing in the fastening system. In particular, the cases of fasteners with or without steel washers are investigated.