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Computer simulations of dislocation glide in a matrix containing coherent spherical precipitates are presented. These particles have a lattice mismatch. Their strengthening contribution (critical resolved shear stress, CRSS) is derived. The size distribution and three dimensional spatial arrangement of the particles are close to those of an actual Ostwald-ripened crystal. An example for such a system is a Cu-rich Cu–Co alloy. The simulations are based on the local stress equilibrium along the dislocation line. The elastic dislocation self- interaction is fully allowed for. Perfect dislocations as well as pairs of Shockley partials are considered. The effect of dislocation dissociation on the CRSS is worked out for large and for small particles. Two particle arrangements of different lattice mismatch and volume fraction are considered. For the simulations of the dissociated dislocation two approaches are used. The first one is straightforward: a pair of partials enclosing a stacking fault is simulated. The second approach is a major simplification which significantly reduces the numerical effort. It is shown that the simplified model comprehends the basic features of dislocation dissociation.