The present invention provides a negative rigidity device capable of adjusting the vibration isolating effect of a vibration isolating construction by being combined with rigidity of laminated rubber body or the like, being easy to return to the origin of a construction after an earthquake or the like, and capable of properly accommodating an intermittent motion caused daily by temperature changes or the like; ; and a vibration isolating construction. The negative rigidity device (10) comprises an upper member (12) provided with a roller (12b) or a wheel, and a lower member (11) formed into ahog-backed shape having a specified curvature and an upward-protruding form, the curvature being smaller in a specified range (11b) including the vertex of the upward-protruding form than in other ranges, wherein the roller (12b) or a wheel of the upper member (12) rolls along the upside surface of the lower member (11) to thereby change negative rigidity when the upper member (12) deforms beyondthe specified range (11b). The vibration isolating construction (30), which can be adjusted in vibration isolating effect and easily restored to the original after an earthquake or the like, can be constituted by providing the negative rigidity device (10) and laminated rubber (32) having restoring force characteristics to a construction (31).