The conservation of historical monuments and especially natural stone masonry arch bridges is an issue which is becoming increasingly important. The prerequisite for any analysis of the load carrying capacity of such stonework is a precise knowledge of its material behaviour. This includes the stress-strain relationship for the natural stone masonry considered as a continuum, with all its important characteristics, such as nonlinearities in the pre-peak and softening behaviour in the post-peak domain. Natural stone masonry is a heterogeneous and anisotropic material which takes many different forms, ranging from rubble to ashlar masonry. Its mechanical behaviour is clearly influenced by its various characteristics. This paper investigates the influence of various parameters such as masonry type, bond, stone type and thickness of joints influence the stress-strain curve of natural stone masonry. It is also shown how stress-strain relationships originally established for brickwork masonry can be adapted to describe the behaviour of other types of stone masonry. Finally, application of stress-strain relationship to predict the load carrying behaviour of natural stone structural elements such as arches will be outlined.