The behavior of masonry structures plays a crucial role in the preservation and conservation of heritage sites, especially in seismically active areas. In this work, the Continuous Airy-based for Stress Singularities (CASS) method is applied to model the response of a masonry façade under different external loading and displacement conditions, including lateral seismic forces. The formulation of a Boundary Value Problem (BVP) for structures composed of unilateral materials, is briefly recalled, then, the CASS numerical formulation is presented, highlighting its distinctive features, such as its ability to model complex stress distributions, especially dealing with stress concentration over curves. The resulting discrete problem is cast as an optimisation problem with conic discontinuity constraints, which is particularly useful for handling complex geometries, such as those encountered in heritage architecture. The presented numerical results not only address the calculation of seismic load multipliers—key parameters for evaluating the seismic performance of structures—but help in discussing various numerical aspects, such as convergence issues and the treatment of irregular geometries.