The overlay model of cyclic deformation is considered to be physically motivated and has definite advantages over the classical models. It can describe qualitatively a variety of effects that the classical models are not able to describe. This model successfully describes the deformation behavior of a material that obeys Masing's hypothesis. However, there are many materials that do not satisfy Masing's hypothesis, and show the cyclic hardening (or cyclic softening) and the strain range dependence. In this investigation, we modified the overlay model to consider the characteristics in the cyclic deformation behavior of non-Masing material, observed through low cycle fatigue (LCF) tests of 316L and 429EM stainless steel. The yield stress of the subelement in the model was divided into two parts: one part describes the master curve and another represents the change of the elastic limit. The memory surface of the plastic strain range was introduced to consider the strain range dependence. The prediction by the modified overlay model shows good agreement with the actual hysteresis loops at a wide range of strain amplitudes and temperatures. (C) 2003 Elsevier B.V. All rights reserved.