Some brittle epoxies can be said to be toughened significantly by a dispersion of rubber particles. Several models have been proposed to explain the role of the rubber particles in toughening. In the present research, by introducing the stereological concept based upon the statistical geometry to the microstructural modeling of the composites and considering the interfacial phenomena between a matrix and a particle, the micromechanical analysis by means of the generalized equivalent inclusion method is made of the rubber particle-reinforced epoxy composite having the crack bridging particles whose radii are various in size. By analyzing the micromechanical model, the critical length a(c) of the matrix crack whose propagation will be arrested, that implies the fracture toughness of such a composite, can be calculated. The effects of the volume fraction of particles and the variance of the radii of particles on the toughness can be evaluated. The results obtained are consistent with the common experimental findings.