This paper presents a method for passing critical speeds of a rotating shaft by use of support springs made of memory metals. In this method the vibrations of the shaft due to whirlings are controlled by use of the on (heating) and off (cooling) heat control of the memory metals which support the bearings. In the analysis, the exact solution is obtained on the problem of a multi-span shaft carrying a disc. Numerical calculations have been carried out for some important problems and experimental tests have been carried out to verify the present control method and the theoretical results.