The realization of mechanical decoupling zones around a membrane to reduce package stresses is presented. Wet-isotropic etching with a nitric/fluoridic solution (HNO3/HF/H2O) as well as reactive-ion etching (RIE) with a sulphurhexafluoride/oxygen (SF6/O2) plasma are investigated to realize deep circular grooves. The shape of the cross section of the groove, which determines the shape of the decoupling zone, can be controlled using the RIE method by changing the etch conditions. It is shown that a large undercut at low pressures as well as a small undercut at high pressures is possible with a SF6/O2 plasma, leading to round or steep sidewalls of the grooves, respectively. Finally a completed bare structure containing a membrane and a surrounding decoupling zone is presented.