A mathematical analysis is presented of the reduction of package stresses by introducing an on-chip decoupling zone. Different configurations of the zones are compared, using the finite-element method (FEM) and analytical models. A reduction of several orders of magnitude is obtained when a deep and thin axisymmetrical corrugation with a V-shaped cross section (a V-zone) is applied as the decoupling zone. Approximate expressions for the stiffness and the force reduction are derived. The application of a membrane pressure sensor with a V-zone as decoupling zone is evaluated. It is shown that the sensitivity of the sensor is not reduced by the addition of the V-zone.