In the high-energy section of the Project X Linac, acceleration of H{sup -} ions takes place in superconducting cavities operating at 650 MHz. Two families of five-cell elliptical cavities are planned: beta = 0.61 and beta = 0.9. A specific feature of the Project X Linac is low beam loading, and thus, low bandwidth and higher sensitivity to microphonics. Efforts to optimize the mechanical design of the cavities to improve their mechanical stability in response to the helium bath pressure fluctuations will be presented. These efforts take into account constraints such as cost and ease of fabrication. Also discussed will be the overall design status of the cavities and their helium jackets. The proposed design of the 3 GeV Project X superconducting (SC) Linac employs 650 MHz five-cell elliptical cavities to accelerate 1.0 mA of average H-beam current in the 160-3000 MeV energy range. The 650 MHz region of the Linac is divided into two sections with two different geometric phase velocity factors: beta = 0.61 to cover the 160-520 MeV range and beta = 0.9 to cover the 520-3000 MeV range. Approximately 40 beta = 0.61 and 150 beta = 0.9 cavities are currently planned for the project. An R&D program is in progress at FNAL, in collaboration with TJNAF and India, to develop the 650 MHz cavities for the proposed Linac design. This R&D program includes the design and fabrication of several beta = 0.61 and beta = 0.9 single-cell prototypes for evaluation prior to production of the five-cell cavities. FNAL has contracted AES to fabricate the beta = 0.9 prototypes, while TJNAF is building beta = 0.61 prototypes of their own design. In the remainder of this paper we will restrict our discussion to the five-cell beta = 0.9 cavities.