In this report formulas are derived for a description of the deformation and stress fields near holes expanded by cold working. The results are compared with values obtained experimentally and calculated using the finite element method. The model of the material includes linear hardening and a yielding behaviour according to Tresca's criterion. Small strains are assumed and the elastic-plastic material behaviour is described using the incremental theory of plasticity. To derive the plane stress solution of the problem Koiters "corner point" model has been used.