We use a mechanical model in the context of Bayesian inference to constrain the relative contribution of driving and resistive regional forces to the observed surface deformation. The finite element model straddles the Nubian-Eurasia plate boundary, is viscoelastic, and has fault zones representing regional active faults. Deformation is driven by velocities of surrounding plates and by lateral variations in gravitational potential energy in all models. The magnitudes of slab pull and trench suction at subduction zones, and of active asthenospheric convection are search parameters. Velocities of our median model fit the observations very well. Slip directions agree with focal mechanisms on most model fault zones. Slip rakes and rates agree only partly with results from previous block modeling studies. We find that significant trench suction forces are required on all trenches. Slab pull is irrelevant, and convective shear tractions have a small imprint on the observed deformation of the overriding plate. The average viscosity of the Eurasian lithosphere is 1.5(±0.5)x1022 Pa.s. Resistive shear traction rates are small along all plate boundary segments, except the Kephalonia fault zone. Shear traction rates are significant along all intraplate fault zones, except the northern branch of the North Anatolian Fault zone. We propose a novel way to estimate the rate at which fault zones accumulate slip deficit. We find that slip deficit rates on model faults range between 1.2 and 4.5 mm/yr.