Abstract The glide of a dissociated dislocation across a shearable coherent fee particle embedded in a fee matrix has been simulated on a computer. The particle and matrix have different stacking-fault energies. The flexibility of both partial dislocations has been fully allowed for. An Al-rich Al-Ag alloy served as a model system. Thus numerical values for the maximum interaction force F 0sim(ρ) between the dislocation and the particle have been obtained; ρ is the radius of its intersection with the glide plane. F 0sim(ρ) is compared with the former analytical function F 0sim(ρ), which had been derived on the basis of the ‘straight-line approximation’. F 0sim(ρ) turns out to be smaller than F 0str(ρ). After a suitable adjustment, F 0str(ρ) can be used to represent the numerical data F 0sim(ρ). Inserting F 0str(ρ) into Friedel's relation for the critical resolved shear stress yields an analytical description of stacking-fault energy mismatch strengthening.