About 100 years ago, Dr. Franz Reuleaux invented the elliptical chuck which made it possible to cut elliptical cylinder in the same as cutting cylinder. This was invented on basis of turning block double slider crank mechanism. For this reason, this chuck had a problem of causing vibration as the rotational speed increased. Therefore, this mechanism could not been put into practical use. In order to overcome this weak point, one of the authors invented a new type of cutting machine for elliptical cylinder. In this paper, first the principle of new cutting machine is described. Next this machine is designed and made for trial. Finally two elliptical cylinders are made for trial and measured by roundness tester. Experiments prove that the principle of the new cutting machine holds true, principle of mechanism of cutting elliptical cylinder, and shows fundamental characteristics of this machine and its possibility for practical utility.