A fluid-filled elastic mount including a first and a second support member elastically connected by an elastic body interposed between, a cylindrical connecting member secured to an outer surface of the elastic body, and a closure member fitted on the connecting member. The closure member cooperates with the elastic body to define a fluid chamber filled with a non-compressible fluid. The fluid chamber is divided by a partition structure supported by the closure member, into a pressure-receiving chamber and a variable-volume equilibrium chamber. A sealing rubber layer is sandwiched between the connecting and closure members, in a direction perpendicular to the load-receiving direction of the mount, assuring fluid-tight sealing of the fluid chamber. The second support member includes a caulking portion which retains the connecting and closure members in the load-receiving direction. A method of manufacturing the fluid-filled elastic mount as described above is also disclosed.