The slip line field theory and the upper bound method based on the associated flow rule for the traditional plastic theory don't accord with the experiment for geotechnical material ,so the non-associated flow rule must be applied to geotechnical material which indicates the stress characteristic line don't coincide with the velocity line. In this paper some problems existing in the slip line field theory and the upper bound method based on the associated flow rule were analyzed. The slip line field theory and the upper bound method based on the non-associated flow rule were deduced according to the generalized plastic theory , which eliminated some inconsistencies in the slip line field theory and the upper bound method based on the associated flow rule for the traditional plastic theory.