The ultimate purpose of this study is to create a new lathe by which roundness≈0, cylindricity≈0 and and surface roughness≈0 can be obtained in turning of aluminium alloy, copper alloy, iron, steel, and so on. At first, in this report, it is analyzed theoretically roundness≈0 turning can be realized by combining the insensitive vibration cutting mechanism and the main spindle system with the hydro-static bearing. And this analytical result can be confirmed by the experiments using a newly developed vibration cutting lathe with the improved main spindle of the cylindrical grinding machine with the hydro-static bearing. The main cutting conditions are as follows: the vibration tool ; in the same direction as that of cutting, frequency ; 21. 52, 28. 72, 30. 15 kHz, amplitude ; 13, 18, 26 rim, cutting speed ; 12, 27 m/min, depth of cut ; 0. 03, 0. 05 mm, feed ; 0. 02, 0. 05, 0. 08 mm/rev, cutting tool material and profile ; carbide tool K 10, (0°, 0°, 8°, 5°, 6°, -4°, 0 mm), (0°, 0°, 10°, 10°, 50°, 40°, approximately 1 mm), etc. Aluminium HB = 26, brass HB= 124, carbon steel HB = 155, stainless steel HB=179 are used. The main results are as follows: 1) The roundness value is decreased to about 1/2-1/10 of that of the conventional cutting lathe by means of the ball or roller bearing. 2) Roundness of 0.4 μm is obtained in these materials. This value of 0.4 μm has made a new record in turning. 3) By this study, it is proved that this new lathe combining the vibration cutting and the hydro-static bearing has the possibility of roundness≈0 turning.