Accurately analyzing the propagation of transverse cracking which causes rail failure is important to ensure train operation safety. Crack propagation until now has been analyzed using methods such as the Finite Element Method (FEM). These existing methods, however require the subdivision of meshes to be executed every time a crack is to be analyzed after new propagation. This paper proposes a crack propagation analysis method using the Boundary Node Method (BNM). The development of the BNM program for 3-D elastic analysis is presented here along with the results of some of its transverse crack propagation analyses.