Abstract: A convoluted flexible support structure is provided which is capable of supplying a lateral to axial spring rate in excess of 1,000 to 1. A support member in the form of a steel disc having a specified number of rather large radius, concentric convolutions and a thickness in the range of from about 0.01 to 0.02 inch has an axial stiffness of about 50 pounds/inch while the lateral stiffness is about 100,000 pounds/inch. The support member may be used to support a vibration device where the lateral motion of the vibrator must be highly restricted while providing relatively free axial displacement of about .+-.0.25 inch.