The stress caused by misfitting particles in thin layers adherent to substrates is modelled. The model assumes an elastically isotropic matrix with holes in which the misfitting particles are introduced. The stress field generated in the matrix consists of a hydrostatic stress resulting directly from the misfitting particles and a biaxial state of stress resulting from the condition that the layer should remain attached to its substrate. The model and its implications for diffraction stress measurements are illustrated using magnetron sputtered TiN layers.