Some kinds of fault tree analysis are described for which cut set enumeration is inadequate. Modularization leads to more efficient computer programs, and also identifies subsystems which are intuitively meaningful. The problem of finding all modules of a fault tree is formulated as as extension of the problem of finding all ``cut-points'' of an undirected graph. The major result is a FORTRAN program (available as a Supplement) which can find modules of a 1000-event fault tree in a small fraction of a second. A generalized module is defined.