Tensile data from polycrystalline samples of copper dispersion strengthened by alumina are analysed. The basis of this analysis is to look at the strain range from 0.05 to 0.20 where the stress-strain curves show a parabolic hardening behaviour and are parallel to one another. The means by which the addition of strength components from various elements of the microstructure and substructure might explain this behaviour are investigated. It is shown that a linear combination of a matrix friction stress, an Orowan bowing stress, a matrix mean stress from the particles and a combined dislocation interaction term can explain this data and also the data from some aluminium-alumina materials. The dislocation interaction term, which dominates, is comprised of terms which cover the pure matrix work hardening, the hardening due to particles and due to the grain boundaries. This term is derived by summing the dislocation density contributions from each of these three sources. The type of additivity suggested here not only gives very good agreement with the stress-strain data but it also uses and is in accord with the experimental measurements of dislocation densities made using transmission electron microscopy.