Provided are a vibration isolating table (1) with damping mechanism having initial rigidity so that a vibration isolation subject is not swayed under a state in which no vibrations act, and configured to function in a case where vibrations act so that the vibration isolation subject can be protected, and a vibration isolating table unit (15) using the vibration isolating table (1). The vibration isolating table includes a fixed plate (2); a guiding member (42) provided so as to be freely movable in an X direction relative to the fixed plate (2); a movable plate (3) provided so as to be freely movable relative to the guiding member (42) in a Y direction orthogonal to the X direction; an X-directional circulation belt (6) configured to circulate in accordance with X-directional movement of the guiding member (42) relative to the fixed plate (2); a Y-directional circulation belt (9) configured to circulate in accordance with Y-directional movement of the movable plate (3) relative to the guiding member (42); and rotary dampers (7, 10) respectively provided to the fixed plate (2) and the movable plate (3), and respectively including rotationally driven members (70, 100) around which the X-directional circulation belt (6) and the Y-directional circulation belt (9) are respectively looped, the rotary dampers (7, 10) being configured to respectively impart resistance to rotational motion of the rotationally driven members (70, 100).