In this paper the factor of safety (FS) and critical line-segments slip surface obtained by the Alternating Variable Local Gradient (AVLG) optimization method was presented as a new topic in 2D. Results revealed that the percentage of reduction in the FS obtained by switching from a circular shape to line segments was higher with the AVLG method than other methods. The 2D-AVLG optimization method is a new topic for finding critical line-segments slip surface which has been addressed in this paper. In fact, the line-segments slip surface is a flexible slip surface. Examples proves the efficiency and precision of the 2D-AVLG method for obtaining the line-segments critical slip surface compared to the circular and circular-line slip surfaces.