With the engineering materials such as sands, soils and cinders in the background, a multi-scale model and corresponding numerical methods with high accuracy and efficiency are developed for numerical modeling of mechanical behaviors occurring in granular materials, on the basis of the computational homogenization method in light of the average-field theory, using for reference the bridging scale method originally proposed as a new multiple-scale method for nano-materials. In the proposed model the discrete particle model using the distinct element (DE) method and Cosserat continuum model using the finite element (FE) method are used to formulate the problems in terms of two scale levels, i.e. the meso- and macro-scales. The second order computational homogenization procedure, which leads to higher order Cosserat continuum in the macro-scale, is developed in the meso-scale. The relations between the macro- and meso-scopic kinematic and kinetic quantities and boundary conditions prescribed on a meso-structural representative volume element are formulated in the proposed high order homogenization procedure. The DE/FE bridging scale method for granular materials is studied.  Coupled meso- and macro- two-scale boundary value problem, general algorithm for global-local analysis and the multi-scale computational method with high accuracy and efficiency are formulated in the frame of thermo-mechanics and the meso-macro consistency condition. The relations between meso- and macro- constitutive models and model parameters for granular materials are determined in terms of existing meso-scopic constitutive models for discrete particle assemblages with given macroscopic elasto- or elasto-plastic models. The developed multi-scale model will be applied to numerical modeling of progressive failure problems of granular materials characterized with strain localization phenomenon.