An encapsulated MEMS device includes stress-relief trenches in a region of its substrate that surrounds the movable micromachined structures and that is covered by a cap, such that the trenches are fluidly exposed to a cavity between the substrate and the cap. A method of fabricating a MEMS device includes fabricating stress-relief trenches through a substrate and fabricating movable micromachined structures, and capping the device prior art encapsulating the device.