Based on von Mises' yield criterion, deformation theory of plasticity and Swift's hardening law, elasto-plastic deformation of variable thickness annular disks subjected to external pressure is studied. A nonlinear shooting method using Newton's iterations with numerically approximated tangent is designed for the solution of the problem. Considering a thickness profile in the form of a general parabolic function, the condition of occurrence of plastic deformation at the inner and outer edges of the annular disk is investigated. A critical disk profile is determined and the corresponding elastic-plastic stresses as well as the residual stress distribution upon removal of the applied pressure are computed and discussed. (c) 2004 Elsevier Ltd. All rights reserved.