The upper bound approach is applied to a simple model for a composite material and an expression for relative strength of a composite is developed. Relative strength of the reinforcing particle, bond strength between particle and matrix, deformation of particles, void formation, and geometrical factors are all considered in the analysis. It is shown that the general expression for composite strength contains the familiar rule of mixtures as a special case. Further examination of predicted behavior shows that strengths equal or very close to the simple rule of mixtures may be expected in some cases; however, for other ranges of the parameters, the strength will never reach the value predicted by the rule of mixtures.