This invention is a device and method to occlude an aneurysm comprising: a laterally-expanding occluding member (such as a relatively-flat balloon, mesh, net, or patch) that is positioned within the parent vessel of the aneurysm and then expanded laterally and a radially-expanding structural member (such as a stent) that is positioned within the parent vessel of the aneurysm and then expanded radially after, or concurrently with, expansion of the laterally-expanding occluding member. Expansion of the radially-expanding member presses and holds the laterally-expanding occluding member into contact with the aneurysm neck, so that the laterally-expanding occlusive member at least partially covers the aneurysm neck and reduces blood flow to the aneurysm. This invention has several potential advantages over devices and methods in the prior art, especially for treatment of wide-neck and fusiform aneurysms.