To provide a vibration isolation device capable of performing stable machining and a combined punch.laser beam machine receiving no influence of vibration when performing punching.

Since a first fitting hole part 41 is pressed, positioned, and clamped in a second fitting hole part 47 relatively through a spherical body 45 by moving either of a first housing 43 and a second housing 49 relatively by a travel means 57, the first housing 43 and the second housing 49 are positioned and fixed to a fixing side with high rigidity. On the other and, since either of the first and second housings 43, 49 is moved in the opposite direction by a positioning travel means 57 and a machining tool side is supported by the first housing 43 and the second housing 49 through an energizing means 53 when the first and second housings 43, 49 are unclamped, generated vibration is absorbed and isolated by the energizing means 53 to offset a rotary moment generated in a base plate when vibration isolation is performed.