Friction stir spot welding (FSSW) is a solid-state joining process in which a rotating tool is pressed against two materials to be joined for creating a spot weld. The rotating tool comprises a pin with a shoulder. The pin gets inserted inside the material, whereas the shoulder rubs on the surfaces of the two materials. The process encounters friction at the pin-workpiece and shoulder-workpiece interfaces. In order to carry out a realistic simulation of the process, the knowledge of friction is a must. In most of the published work, scant attention has been devoted to the quantitative determination of friction force. This article proposes an inverse approach to the determination of friction force in FSSW. It is assumed that the frictional behaviour at the pin-workpieces interface is sticking in nature and at times, there is a possibility that frictional shear stress is more than the shear strength of the materials due to welding of asperities. This aspect is analysed by carrying out a number of finite element simulations using DEFORM-3D on a shoulder-less pin and validating it through in-house experiments. Later on, a hybrid friction model (combination of Coulomb’s and constant shear models) is used on the shoulder-workpieces interface. The friction parameters are adjusted through an optimization approach by minimizing the error between experiments and simulation. In a typical case, the friction factor (m) on the pin-workpiece interface was found to be 1.05. Friction at the shoulder-work interface was best represented by a hybrid model, with m = 0.77 for the high-pressure region and µ = 0.29 for the low-pressure region, where µ is the Coulomb’s coefficient of friction. Computations with estimated friction predicted temperatures with a reasonable accuracy. It also predicted fairly accurate torque for a tool of different size.