This study presents a set of "particular" strength criteria of the constituent elements of masonry as a composite material constituted by homogeneous fragments of heterogeneous materials (brick and mortar) and contact interface (shear and normal adhesive strength). This paper proposes the expressions for calculate the values of each particular strength criterion used for the discrete modelling of masonry. The results were obtained based on the experimental study of stresses and failure modes in masonry specimens, mortar samples and brick units. There are determined a set of 8 particular strength criteria, which correspond to the actual work of the masonry constituent elements. Their use in the structural micromodelling of masonry allows to determine the body contact interactions, track the gradual accumulation of local stresses, exclude from the calculation model the elements in which a particular strength criterion has been exceeded, and modelling the degradation process.