This paper concentrates on investigating the mechanical stability of a Beam Position Monitor (BMP) support prototype of the Shanghai Synchrotron Radiation Facility (SSRF) project. Both nite element analysis and vibration measurements have been performed. Inconsistent results between the simulations and experiments motivate us to study three connections between the support and the ground: ground bolt (used in the initial design), part grout and full grout (proposed in the later research). After changing the connection, the rst eigenfrequency is increased from 20.2Hz to 50.2Hz, and the ratio of the integrated RMS displacement (4|50Hz) is decreased from 4.36 to 1.23 in the lateral direction. The mechanical stability is improved greatly.