A fluid-filled elastic mount including mutually spaced-apart first and second support members, and an elastic body for elastically connecting the first and second support members. The elastic mount has a plurality of fluid chambers filled with a non-compressible fluid and communicating with each other through an orifice passage or passages, and an air-tight operating chamber which is formed on one side of a flexible membrane remote from the corresponding fluid chamber. This flexible membrane consists of a fluid-impermeable first flexible layer which is corrosion-resistant to the non-compressible fluid, and a fluid-impermeable second flexible layer which is corrosion-resistant to gasoline. These flexible layers are superposed on each other such that the first flexible layer is exposed to the fluid chamber while the second flexible layer is exposed to the operating chamber. The elastic mount further includes a pressure control device for applying a vacuum pressure to the operating chamber so as to restrict elastic deformation of the flexible membrane.