Historical masonry structures constitute a vast array of the historical cultural heritage worldwide. The interest in their preservation pushed researchers to develop theoretical and numerical methodologies for the structural assessment of such constructions. From a numerical point of view, the topic is challenging. Any numerical method must allow an accurate representation of the masonry material by taking into account its strong nonlinearities, orthotropy, texture. In particular, ancient masonry structures are often composed of bricks or stones and dry joints. In this context, limit analysis is a particularly suited tool, since it allows to evaluate the collapse behaviour and the structural safety with very few input parameters. Here we present the assessment of historical dry-joint masonry structures through an upper bound limit analysis numerical approach currently under study. A given structure is represented as a continuous model discretized with planar elements whose kinematics is composed of a rigid body motion and a plastic deformation. The material properties are correctly represented thanks to a homogenization procedure, which imposes the compatibility between the plastic deformations and the kinematics of the corresponding heterogeneous masonry material. The potential of the method is shown through some numerical examples. Promising results have been found even in the case of irregular geometries, which are usual in historical structures.