The present invention is directed to a method for treating aneurysms in vascular tissue. The method includes administering a bisphosphonate compound to a subject in an amount which is effective against the formation or progression of aneurysm, or which is effective to induce regression of an established aneurysm. In alternative methods, an anti-RANKL neutralizing antibody is administered to the subject to achieve analogous anti-aneurysm effect. The methods of particular advantage in the treatment of subjects having an abdominal aortic aneurysm, a relatively common, and life-threatening, condition.