In this paper, we have given a computer program to calculate minimum crossing number provide a measure of complexity for braids. The computer program uses Berger algorithm which uses Artin braid word B of minimal length. Given a braid on N strings, the program generates an Artin braid word to minimal length. The length of an Artin word equals the number of crossing seen in a braid diagram. In this paper we have applied the program for 3-braids and given an example. (C) 2002 Elsevier Inc. All rights reserved.