In this paper, an elastic plastic behaviour model based on internal state variables is investigated. The final aim is to describe the mechanical stress-strain cyclic response of oxide dispersion strengthened (ODS) steels during the cold pilgering process. In this tube forming operation, a material element undergoes a series of small incremental deformations, alternatively under tensile and compressive stresses. The cyclic model considers isotropic hardening and kinematic hardening which can be related to the typical continuous cyclic softening of the ODS steels. Moreover, the identification process of the cyclic model parameters involves experimental data from only one sample. ODS steels tubes usually reveal an anisotropic strength in the radial, ortho-radial and longitudinal directions due to a crystallographic and strongly elongated grain morphology in the rolling direction. Identification of 3 Hill's parameters is done using compression tests of cylindrical specimens cut in three different directions (longitudinal, radial and ortho-radial) combined with an inverse analysis. © 2011 Published by Elsevier Ltd.