A tethered cover airbag system is provided for motor vehicles and the like having a panel formed with an opening in the vicinity of an occupant's seat and including an inflatable airbag mounted in a housing or canister for containing the bag in a deflated condition. The housing has an open end aligned with a panel opening to permit the airbag to pass outwardly when deployed for cushioning support for an occupant in the adjacent seat. A cover is provided for normally closing the panel opening to protect the airbag and is bodily movable to uncover the opening during airbag deployment. A flexible tether is interconnected between the cover and the panel edge or the housing for limiting the movement of the cover away from the panel during deployment. A suitable attachment system is provided for spreading the load exerted by the tether over a large area of the cover for reducing stress exerted on the cover during airbag deployment. The tether thus restrains the cover from moving around the passenger compartment of the vehicle in an uncontrolled manner during an airbag deployment and by reducing the load or stress exerted on the cover by the tether, the chance of break-up or fracturing of the cover into pieces is minimized.