This doctoral thesis aims to develop and use multiscale methods to simulate and predict the clay nanocomposite behaviours. The use and development in multiscale methods provide not only a better underestanding of material properties , but also facilitates the future design of such materials, i.e. computational materials design. First, some epoxy and clay nanocom- posite samples with different clay concentration were built and the mechanical properties were measured. Using these results, the damage and fracture of nanocomposite samples in macro scale were simulated and compared with the obtained test data. To facilitate the implementation and use of multiscale modeling, an open source code is developed which uses the eXtended Finite Element Method (XFEM) to simulate the cracks. Since there are many uncertainties in determination of physical, mechanical and geometrical properties of clays, in this research a combination of micromechanics and stochastic methods were used to predict the elastic modulus and damage parameter of fully exfoliated clay nanocomposites. Next, a semi-concurrent approach for modeling damage in the clay nanocomposites is presented. This method bridges the meso-scale to the macro-scale by a homogenized damage parame-ter. Finally, a concurrent multiscale method is introduced and implemented for 3D dynamic applications. The investigation showed that the proposed method can accurately simulate the crack in the different scales and the spurious wave reflection from coupling region is minimum. Keywords Multiscale analysis, Clay nanocomposites, Micromechanics, Arlequin method.