Hybrid masonry structures combine the ductility of steel components with the shear strength of reinforced masonry panels. The goal of this research is to provide a sound basis for the design of an optimal type of hybrid structure that can be implemented as a new lateral-force-resisting system in high seismic regions. The most challenging part in the hybrid structure simulation is to capture the behaviour of concrete under different loading scenarios. This thesis sets up a computational framework for the analysis of hybrid masonry systems using an improved non-local technique, including the contributions such as: adopting the consistent linearisation technique to improve the computational efficiency of the non-local one-scalar damage model; presenting a new way to calibrate parameters in the tension damage law in the two-scalar damage model by correlating them to the ones in the one-scalar damage model; designing a data structure to save the domain information for each material point in order to apply the non-local technique; proposing an automatic parameter calibration procedure based on the Nelder-Mead simplex method for the two-scalar damage model utilizing the global system testing data; proposing and identifying the internal variable to be non-localized to enhance a new damage model to obtain the mesh regularization solution. Finally, this thesis performs a system-level numerical study of the energy dissipation mechanisms of hybrid masonry structures under cyclic loading. The numerical studies extrapolate test data to a wider range of structural configurations in terms of various connector strengths and different masonry panels to maximize seismic energy dissipation. This work also investigates the influence of the load transfer mechanism on the lateral strength, stiffness, energy dissipation capacity and deformation pattern of the hybrid system. Findings from the numerical studies performed in this work confirm the feasibility of using hybrid structures in high seismic areas.