Zipper defects are sometimes encountered during the production of thin walled tubes by the cold drawing process. Production experience suggests that occurrence by these defects can be reduced by changing lubrication conditions and drawing velocity. In this paper, a 2-D finite element package DEFORM was used to model the multi-pass drawing of small diameter copper tubes. The effect of various processing conditions such as the effect of annealing, lubrication, drawing speed, die design and pass sequence on the principal stresses, damage factors and maximum temperatures in the tube were investigated. It is found that annealing, die design and pass sequence design can be used to reduce the tube stresses and thus eliminate the zipper defect.