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Dislocation glide in a metal matrix with spherical precipitates has been simulated on a computer. The critical resolved shear stress (CRSS) ‰ p is derived, and the superposition of two strengthening effects is investigated. Firstly, the precipitates are incoherent; they cannot therefore be sheared but are overcome by the Orowan process (dispersion strengthening). Secondly, the precipitates have a size mismatch and the respective elastic stresses inhibit dislocation glide (size-mismatch strengthening). The simulations are based on the local equilibrium of resolved stresses in one glide plane and the elastic dislocation self-interaction is fully allowed for. The size distribution of the particles and their arrangement in space are very close to those of an actual Ostwald-ripened crystal. The mean particle radius, their volume fraction and the constrained size mismatch parameter are varied in wide ranges. The CRSS is presented as a function of these three parameters and an empirical law of superposition is proposed.