Detailed micromodel simulations of stone masonry walls require as input a 3D mesh that represents a realistic arrangement of stones in the masonry wall. In this paper, we constructed the first 3D masonry microstructures to derive 2D and 3D finite or discrete element meshes for a large range of stone and brick masonry typologies. The generation process was treated as a constraint many-objectives packing optimisation problem, which was designed to mimic the building process of a mason. The generated walls were compared qualitatively and quantitatively with real stone masonry samples of regular and irregular typologies. The Python3.7 codes of the microstructure generator and the generated meshes shown in this paper are all made available under GNU LGPLv3 terms and conditions. The techniques in this paper for generating 3D meshes of stone masonry walls will serve as input for simulations of individual walls, multiscale analyses of entire structures as well as for homogenisation techniques.