A significant number of scientific research groups are still nowadays dealing with masonry material as the main focus of study since it provides an open field of research that is far from resolution in a standardized manner. As masonry structures are highly vulnerable to any level of natural hazards, especially seismic activity, both traditional and composite materials have been used as reinforcements in masonry and provide different solutions that meet the key requirements set out by cultural heritage organizations. Extensive effort has gone into developing appropriate techniques of assessment, that usually demand an individualized methodology of analysis which is to be handled through comparative studies requiring results validation. A suitable field of study is the Limit Analysis approach towards masonry structures, as it offers quite accurate and, more importantly, robust results regarding the necessity to resolve the issues involved in the masonry numerical representation so that reliable outcomes are drawn to enable the assessment of such structures. The enrichment of a Limit Analysis homemade code with the inclusion of cohesion and frictional behaviour at the interface level is able to account, in a simplified but very robust manner, the perplexing issues involved with the numerical assessment of reinforced masonry structures with particular reference to arches. The cohesion incorporation is calibrated for a variety of in-plane applications, accounting for the joints’ indirect tensile strength, that is able to simulate the strengthening measures. Results obtained are validated with literature results and included in a comparative study between discrete numerical models that utilize different modelling strategies.