Gas diffusion barriers (GDB) are essential building blocks for the protection of sensitive materials or devices against ambient gases, like oxygen and moisture. In this work, we study the mechanics of GDBs processed by atomic layer deposition (ALD). We demonstrate that a wide range of ALD grown barrier layers carry intrinsic mechanical tensile stress in the range of 400-500 MPa. In the application of these GDBs on top of organic electronic devices, we derive a critical membrane force (sigma . h)(crit) = 1200 GPa angstrom (corresponding to a layer thickness of about 300 nm) for the onset of cracking and delamination. At the same time, we evidence that thicker GDBs would be more favorable for the efficient encapsulation of statistically occurring particle defects. Thus, to reduce the overall membrane force in this case to levels below (sigma . h)(crit) we introduce additional compressively strained layers, e.g., metals or SiNx. Thereby, highly robust GDBs are prepared on top of organic light emitting diodes, which do not crack/delaminate even under damp heat conditions 85 degrees C/85% rh.