To provide a base isolation element, a building with a base isolation element and a base isolation element control method, capable of absorbing a horizontal vibration applied from a foundation to a structure, and preventing the lift of the structure from the foundation upon the occurrence of an earthquake with a simple constitution.

A parallel link mechanism 11 is laid between a base isolation element support means 5 and a base isolation support plate 4, and the means 5 and the plate 4 are made to relatively travel in a horizontal direction via the parallel link mechanism 11, upon exposure to the horizontal vibration of an earthquake inputted to a foundation 2, thereby absorbing a horizontal vibration applied from the foundation 2 to a building 1. The building 1 is prevented from being lifted on the operation of the parallel link mechanism 11.