A device for excluding the left atrial appendage (LAA) includes first and second members, each with first and second ends. The second ends are connected by a hinge. The first ends interlock to close the device about the LAA. The members are shaped such that they can exclude the LAA without causing the development of necrotic tissue. If desired, a flexible cover can be provided and the first and second members can be disposed within the cover. If such a cover is used, it will contact the LAA in order to cushion the contact between the members and the LAA and minimize the tendency of the LAA to bleed. The invention also includes methods for using the device to exclude the LAA.