Hypersonic aircraft are subjected to extreme conditions with respect to mechanical thermal and acoustic loads. Materials with complex microstructure, such as Functionally Graded (FGM) and honeycomb, are expected to play a key role in such vehicles. Detailed numerical stress and thermal analysis of such materials, with conventional Finite Element Methods (FEM), is extremely difficult. The Fast Multipole Boundary Element Method (FMBEM) is a very promising candidate for carrying out such calculations efficiently and accurately. This is an O(N) method (where N is the size of a problem) with respect to both matrix formulation and solution of linear systems. It is proposed that two user-friendly software packages based on the FMBEM, to be called AvantFGM and AvantHoneycomb, will be developed in this proposed Phase I project. These packages will be used to carry out mechanical and thermal characterization of these complex materials. The output of these packages will deliver material properties as functions of spatial coordinates, which can then be used to carry out conventional FEM analyses of aircraft components of complex geometrical shape. Plans for Phase II call for development of fully functioning commercial software capable of analyzing many realistic situations pertaining to hypersonic aircraft. Phase III will be concerned with further development of the software to include damage accumulation (due to, for example, mechanical, creep and thermo-acoustic fatigue) and risk analysis.