The objective of this paper is to evaluate the crack stability of the nuclear main stresm pipes, considering the load reduction effect due to the presence of circumferential throuth-wall crack. Also, the optimization techniques are adoped tosimulate the crack effect on the elbow component of the piuping system. By using a general beam elemetn which contains a discontinuous cross-section, the piping analysis is accomplished to acquire the reduced load. Considering this reduced load, it is feasible for the LBB application in nuclear main stresm pipe. Also, by combining an optimization program and a genaral finite element analysis program, the appropriate dimensions of the simplified beam elemtn which represents the effect of crack in elbow could be successfully determined.