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The glide of dislocations in peak- and overaged particle strengthened f.c.c. materials has been simulated in computers. The resistance of dislocations to bending has been described on the basis of Brown's (Phil. Mag.10, 1964, 441) concept of the dislocations' self-stress. Hence even strongly bent dislocations have been treated accurately. The computer experiments have been conducted for three different types of spherical particles: (i) incoherent, i.e. non-shearable ones, (ii) long-range ordered shearable ones, and (iii) ones which have a lattice mismatch. The finite dimensions of the particles have been fully allowed for. These simulations yield numerical data for the critical resolved shear stress as a function of the volume fraction of the particles and their average radius. These functions can be well represented by amended versions of current analytical formulae derived from standard models of particle strengthening.