The problems related to the analysis of ancient constructions are gigantic due to the difficulties in characterizing the geometry, the materials, the sequence of construction, the existing damage and the building processes. A difficult aspect in the repair and strengthening of existing structures is the long-term behaviour of masonry. Safety assessment has been greatly influenced by the collapse of monumental buildings in the last decade, where creep behaviour and creep-fatigue interaction proved to be of relevance for massive masonry walls. Experimental testing on the creep of regular and rubble ancient masonry together with numerical modelling is currently under investigation by the authors. In a first stage, the research is primarily focused on the monotonic behaviour. This represents a contribution for understanding creep behaviour, providing insight into the basic phenomena that occur in masonry upon increasing loading. The results obtained using a continuous model to represent the masonry components largely overestimated the experimental strength and peak strain. Alternative modelling approaches seem, thus, to be needed and a discontinuous model in which a fictitious micro-structure was given to the components was considered. Clear advantages were shown by this last model. In the present paper, the results obtained using these models are briefly reviewed. The results from the ongoing simulations on the long-term behaviour of masonry assemblages will be presented in the oral communication.