An airbag device includes a gas generator and an airbag to be accommodated behind at least one cover that can be displaced from a closed position, in which it is integrated into the vehicle's paneling, into an open position, in which it is disposed behind the paneling, when the airbag device is activated by driving devices. In the open position, the cover does not substantially project beyond the vehicle's paneling in the direction toward a passenger. The driving devices include at least one rolling piston that can be rolled in a guide chamber along a rolling path from a starting position into an end position when being subjected to compressed gas. The rolling piston thus causes the cover to move from the closed position to the open position. A method for operating an airbag device is also provided.