Nano-scaled matrix additives, such as nanoparticles and nanotubes, can considerably improve the mechanical properties of polymers. However, the exact mechanisms leading to the increased properties have not been completely understood. Two effects, which play a minor role in the prediction of the elastic properties of nanocomposites so far, are the formation of a particle-matrix interphase and agglomeration of nanoparticles. Based on the literature, both can be assumed to considerably affect the molecular structure and the mechanical properties and should thus be included in the material design process. In this thesis, a hierarchical multi-scale framework for the prediction of the elastic nanocomposite properties is developed. It incorporates the previously mentioned effects and contributes to a more realistic numerical modeling and simulation of nanocomposites. Starting on the atomistic level, the elastic properties of the constituents of the nanocomposite, namely the nanoparticle, the bulk polymer and the nanoparticle-polymer interphase, are characterized. Besides classical virtual material tests, two new simulation approaches are developed. Simulating atomic force microscopy allows for a direct comparison to nano-scaled experiments and can thus contribute to a better understanding of the acting principles. To overcome associated restrictions, a new approach for the direct calculation of the mechanical interphase properties based on molecular dynamics simulations is introduced. The findings and the homogenized elastic properties from the atomistic scale are sequentially transferred to the microscale, on which models with three levels of detail are investigated. Representative volume elements containing a homogeneous primary particle distribution are used for calibrating the finite element simulations and for studying the influence of the interphase on the elastic nanocomposite properties. By introducing agglomerate unit cells and representative agglomerate volume elements, the influence of agglomeration and the agglomerate size distribution can be incorporated step by step. To additionally study the effect of resin-free areas inside the agglomerates, coupled simulations are developed, which combine the fundamental ideas of the finite and discrete element method. The whole multi-scale framework is demonstrated for a boehmite/epoxy nanocomposite. Because of the small scale, a consistent and direct validation is not feasible with existing experimental methods and results. With the current assumptions, the elastic nanocomposite properties can be predicted with a lower bound, which provides a good approximation of the macroscopic experiments, and an upper bound, which shows the potential of the nanocomposite. Due to the modular implementation of the model generation, the framework can easily be enhanced by possible new findings.