The Navy Prototype Optical Interferometer (NPOI) near Flagstaff, Arizona, makes use of separate smaller optical elements spaced along a Y-array and used simultaneously to simulate an equivalent single large telescope. The instrument is useful in generating and upgrading existing astronomical catalogues and investigating synthetic aperture optical imaging techniques. The NPOI is a joint collaboration between the US Naval Observatory and Naval Research Laboratory in collaboration with the Lowell Observatory. Stellar radiation (visible light) reflects off 35 cm diameter flat mirrors, also known as siderostats, toward a tilt-tip mirror, which reflects a 12 cm diameter beam through a multi-reflection relay transport system. To maximize the reflective area of the siderostat optics and achieve an increase by a factor of 8.5 in light collecting area, a beam compressor is to be installed between the siderostat and fast tip/tilt mirror. However, the present configuration of a prototype beam compressor mount (BCM) vibrates at unacceptable amplitudes, which makes it nearly impossible to optically align the mirrors. This paper presents the results of finite element analyses conducted to quantify the design limitations of the prototype beam compressor mount. The analyses indicated that the current configuration is too soft, with very low fundamental frequencies, which verified the difficulties encountered during alignment tests. Based on these results, design modifications have been proposed to increase the overall structural stiffness of the mount and increase its fundamental frequency of vibration. These modifications will mechanically stabilize the structure for the alignment of the optics, and allow integration of the compressor into the interferometer. The interferometer will then have the capability to capture more light from each siderostat and allow observations of fainter stellar targets. More generally, the results can be useful as a guide for engineers and scientists involved in the design of similar optomechanical structures.