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SUMMARYMethods for the analysis of complex, highly redundant structures subjected to intermittent loads causing biaxial membrane stress and stress reversal into the plastic range are presented. The Bauschinger effect in multi-axial stress is taken into account by the use of Ziegler's modification of Prager's kinematic hardening theory. The implementation of this plasticity theory in the discrete element methods involves the application of the loading in small increments. A linear relationship between increments of plastic strain and of stress, arising out of the theor is used in conjunction with a linear matrix equation that governs the elastic behaviour of the structug. In the latter equation, plastic strains are interpreted as initial strains. A solution to the linear matrix' equation, expressed in terms either of stress or of total strain, may be obtained by utilizing one of two alternative procedures. The methods are capable of treating materials which exhibit elastic-plastic behaviour involving ideal plasticity, linear or non-linear strain hardening, or limited strain hardening. Application is made to several representative structures. Comparison of some of the results with existing test data for both monotonic and reversed loading shows good correlation.