In this paper, we review recent advances in mathematical and computer
science techniques for modeling crack propagation in solids. The fract
ure mechanics aspect of this problem is attacked by boundary integral
equation methods, in particular the use of hypersingular integral equa
tions for analyzing crack geometries. Key issues in the development of
a software system capable of efficient crack propagation studies are
also discussed. As an illustration of these techniques, calculations a
nalyzing crack growth in a fuel door hinge on the Space Shuttle are pr
esented.