Material properties for composite structures, such as biological materials and advanced polymers, can be found using multiple techniques and at different length scales. Due to the need to reconcile measurements at multiple scales, various techniques for multiscale modeling are presented. One imaging technique, magnetic resonance elastography, is a non-invasive imaging method to determine tissue properties in vivo. The process of elastography involves the inversion of a nonlinear problem, which necessitates assumptions about the underlying material. In order to improve the fidelity of the elastographic techniques, a finite element model describing the micromechanics of the microstructure of the brain is presented. To demonstrate our approach, a two-dimensional representation of a periodic array of myelinated axons embedded in homogeneous glial matrix is modeled. Confirmation of the numerical codes and a homogenization scheme is carried out via simple test cases. Due to architectural similarities between axonal white matter in the brain and fiber composite materials, the same technique is implemented for modeling of a Kevlar polymer fiber. For the fiber, a representative nanoscale cell for Kevlar fibers is developed that captures the fibril and microfibril structures. In this regard, a finite element model that describes the nanoscale structure of Kevlar fibers was devised to predict their macroscale response. As with the biological materials, it is important to characterize the effects of changes to the microscale behavior and geometry on the macroscale response. To this end, sensitivity analyses are performed to inform areas of future experimental design, research, and development. By using multiscale techniques in combination with relatively simple microscale models, it is possible to perform many calculations in a short amount of computational time, lowering both the cost and time investment for complex models. In addition, by implementing similar techniques and geometry for differing materials, it is relatively straightforward to develop multiuse, high fidelity models.