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Masonry is one of the most commonly used construction materials for residential buildings and historic buildings around the world. Some of these buildings are located at seismic zones, while unreinforced masonry structures are vulnerable to seismic loads. To assess the existing masonry buildings and to design new masonry structures, nonlinear seismic simulations are conducted with macro modelling or micro modelling approach. The macro modelling approach, which smears out the details of the bricks and joints as a homogenous material, can efficiently and robustly model complete masonry structures. A commonly used orthotropic constitutive model is the Engineering Masonry Model of the DIANA FEA, which is based on the Total Strain Method that eliminates the mapping-back process in conventional elastoplastic constitutive models. The micro modelling approach, which explicitly models the bricks and joints, can better represent the mechanical behaviours of masonry. However, most of the constitutive models used in micro modelling are based on elastoplasticity that usually causes numerical difficulties due to its mapping-back process. The lack of a robust constitutive model has severely hindered the application of this accurate analysis approach. So, this thesis proposes a sub-increment based iterative constitutive model for interface elements, based on Multi-surface Plasticity Criterion. This model aims to enhance the robustness and accuracy of the constitutive model used for micro modelling. It eliminates the conventional mapping-back process in elastoplastic constitutive models by introducing the ideas of sequential uni-axial loading algorithm and an extra damage iterative calculation algorithm. These algorithms are robust even when the stress state is at the corners of the yield surface. The model also introduces the concept of sub-increments to consider the path dependency in plastic process. All the formulations of this constitutive model are derived based on a