Unreinforced masonry (URM) is inherently vulnerable to seismic forces due to its minimal ability to resist tensile forces. Typical structural design features in URM buildings such as torsional irregularities and re-entrant corners increase this vulnerability. This thesis seeks to address the seismic vulnerability of URM structures due to plan irregularities and to contribute to the structural engineering knowledge required to lessen the need for new construction by supporting the reuse, rehabilitation, and ongoing maintenance of existing buildings. A comparative analysis based on the results of nonlinear static and incremental dynamic analyses was carried out on numerical models representing URM structures with plan irregularities typical in Ottawa, Canada. The results from these analyses determined that damages to the structure and the probability of collapse of the structure were reduced overall with the minimization of torsion and full lateral support of the re-entrant corners in the modelled structures.