Several continuous and discontinuous micro-modelling approaches for masonry assemblages are currently under investigation by the authors. The aim is to find a model that provides a suitable description of the material behaviour under compression. Firstly, the behaviour under short-term loading is being considered and, in a later stage, also long-term loading will be addressed. The present paper illustrates the recent advances in the research, focused on the assessment and application of a proposed discontinuous model to the simulation of uniaxial compression tests of masonry prisms. In this model, a fictitious micro-structure composed by linear elastic particles separated by non-linear interfaces is adopted to model units and mortar. The main results obtained and their critical discussion are given in the paper.