Abstract: In this paper, based on the three-dimensional flow theory of plasticity, the fundametal equations for plane strain problem ofelastic-perfectly plastic solids are presented. By using these equations the elastic-plastic fields near the crack tip growing step-by-step in an elastic incompressible-perfectly plastic solid are analysed.The first order asymptotic solutions for the stress field and velocity fields near the crack tip are obtained. The solutions show the evolution process of elastic unloading domain and the development process of central fan domain and reveal the possibility of the presence of the secondary plastic domain. The second order asymptotic solution for stress field is also presented.

Key words: microtubule buckling, orthotropic Winkler-like model, elastic medium