Masonry is one of the oldest building materials, but there are many unsolved problems regarding the basic strength and deformation behaviour. The paper focuses on the different masonry qualities both in Europe and the USA by comparing the discontinuous, non-linear behaviour of masonry as a jointed block structure with other building materials, e.g. rock mass. Basic principles and statements dealing with the compressive (uniaxial, biaxial) and shear strength are derived. Taking into account the complex structure and the large variety with respect to block sizes, block qualities, mortars, bond forces and the overall geometry the designer is obliged to use alternative modelling techniques to the finite element method (FEM). One alternative is the distinct element method (DEM), which allows large rotations of the blocks and large deformations, e.g. separations in and of the joints. This method is well established for analysing rock masses but, as demonstrated in this paper, it is well suited also to the investigation of masonry failure mechanisms. The discontinuous non-homogeneous behaviour of masonry can be modelled very well, and the results compare favourably with respect to real cracking behaviour.