Abstract: According to Iliushin's small elastic-plastic deformation theory,in this paper,we derive the basic equations of plane-strain problems in a power hardening and incompressible material.In addition,this paper presents two methods to solvethese basic equations,i.e. the displacement function_stress method and the stress function_strain method. Twoexamples have been calculated to illustrate the application of these two methods.

Key words: Birkhoffian system, sympletic algorithm, canonical transformation