A high strength buckable rivet made of an alloy consisting of titanium and columbium, the optimum proportion being about 55% titanium and about 45% columbium. The method of making this rivet includes the steps of cold forming a cylindrical blank so as to form a head and shank of the rivet and cold working the head and a portion of a shank of the rivet so as to leave a ductile tail portion capable to form a buck tail, the optimum length of the ductile portion being about 0.8 times the diameter of the rivet shank.