In recent years, the world has paid great attention to the utilization of ocean space and development of marine resources such as petroleum, natural gas, wind resources and sea metallic minerals. For our nation, protection of the marine environment and development of marine resources has become an important strategy of sustainable development. However, in harbor and offshore engineering, the loading condition of the foundation is very complex (the foundation is usually subjected to vertical and horizontal loads as well as moments where the vertical force is resulted from the weight of the superstructure while the horizontal load and moment are induced by wind and wave forces or earthquake inertia force), and the seabed is often consisted of distinct layers with significant different properties. Therefore, in foundation design of large marine structures (e.g. deepwater harbor, marine platforms), soil properties and loading conditions shall be taken into account in details. In this research project, the main objective is to investigate the stability of the offshore foundations subjected to complicated conditions. In the study, through numerical calculation, theoretical analysis and indoor model tests, the relationship between the bearing capacity, the failure mechanisms and the footing-subsoil interactive behaviors, the strength character of subsoil and the loading conditions is illustrated. Numerical analysis procedures have been established to calculate of the bearing capacity of foundations under combined loading. Based on the procedures, parametric studies have been performed, and diagrams and simplified formulae for the bearing capacity of foundations are obtained, which can be used to develop and improve the design of offshore foundations. Meanwhile, according to sub-loading theory, ALPHA constitutive model is improved to be able to simulate complicated deformation behaviors of soil before yielding. Based on the improved constitutive model, a pseudo-static finite element procedure is established to calculate the cyclic bearing capacity of foundations. Using this procedure, the bearing behaviour of foundations on homogeneous subsoil under cyclic loading is discussed.