The impact of advanced materials on human society is tremendous. Development of new materials can bring about innovations in many engineering branches, enabling better designs for structures, equipment and devices. Computer modeling and analysis play a significant role in the understanding and characterizations of many advanced materials. Boundary element method, as a boundary-type computational method, offers some unique features that are most advantageous in material modeling. In this dissertation, both 2-D and 3-D multi-domain boundary element programs are developed for the analysis of various advanced materials. The 3-D multi-domain boundary integral equations (BIEs) formulation for thermo-elastic problems is established. A new proof of the non-degeneracy of the BIEs for general elasticity problems with thin shell-like structures is provided. Related numerical issues for more accurate and efficient evaluations of various nearly-singular integrals that arise in thin material regions using the BIEs are addressed. Convenient visualization tools are also developed to facilitate the pre- and post-processing for BEM applications. Numerical examples using the developed multi-domain BEM, ranging from stress singularity issues in thin multi-layer coatings and thin films, effects of thin interphases in fiber-reinforced composites, load transfer studies in short-fiber and particulate reinforced composites, to the characterization of carbon nanotube-based composites, are presented to demonstrate the high accuracy and efficiency of the developed BEM in the analyses of advanced materials.