The aim of this paper is the development of suitable mechanical models able to reproduce and, hence, to predict the response of masonry structures. In particular, the study is addressed to the modelling of strengthened masonry structures in which the introduction of new types of reinforcement, particularly the FRP (fibre-reinforced plastic) materials, strongly affects the structural response through complex interaction mechanisms between masonry and strengthening elements. In this paper two different approaches able to model the behaviour of un-reinforced and reinforced masonry structures are proposed. The first one is based on a micro-mechanical and multiscale analysis combined with the use of the kinematic and static theorems of the lim...