We illustrate some of the alternatives existing, and difficulties to be expected when studying the behaviour of old masonry buildings numerically, especially in the non-linear range. Even if, nowadays, several quite sophisticated, continuum, discrete or interface constitutive models for masonry/mortar/dry blocks exist, the difficulty of properly applying them to real situations suggests the use of simpler approaches, such as elasticity or elastoplasticity as a starting point. Even in these simplified contexts, however, the analysis of old masonry poses several problems, some of which are illustrated by means of application examples, first with reference to the analysis of masonry walls, then with reference to the analysis of arches and vaults. The importance of properly taking into account the effects of design and construction details on the overall behaviour is stressed, as well as that of complementing the numerical results with analytical, simplified estimates of the structure behaviour, such as those given by the methods of the thrust line or limit analysis, when applicable.

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