Ultra-stable lasers have become useful tools in frequency metrology and precision physics experiments such as optical clocks, optical frequency synthesizer, optical microwave generation, gravitational wave detection, and tests of fundamental physics. In these applications, lasers are required to have ultra-narrow linewidth and ultra-high short-term stabilization. To this aim, a laser is usually servo-locked to a high-finesse Fabry-Perot cavity by Pound-Drever-Hall (PDH) method. Thus the frequency stability of the laser is determined by the length stability of the cavity itself. Environmental vibrations especially due to low frequency (below 100 Hz) seismic and acoustic accelerations are one of those dominant noise sources, which result in quasi-static deformations of the cavity and then degrade the stability of the optical length between two mirrors. Ingenious and elaborate designing both in cavity spacer structure itself and its supports are necessary to decrease its vibration sensitivity. Here we report a tetrahedron-like optical reference cavity design that is insensitive to vibrations in all direction and to constrained force on the four support vertices of a tetrahedron. The ideal optimal cavity structure isobtained by truncating the cubic vertices to make the cavity length insensitive to the pressuring force. In the finite element analysis, the deformation due to low-frequency noise can be considered as the static case where a gravity-like force is appliedto the cavity. Thus the method can give quantitatively the acceleration sensitivity of the ultra-stable optical reference cavity. The calculated acceleration sensitivities for an ideal version of the mounted cavity are 0.1×10-11/g, 1.8×10-11/g, and 1.8×10-11/g (where g=9.81m/s-2) in the optical axis and two transverse directions. The high-fold symmetry of the cavity itself and the structural support can well constrain the rotation and translation freedom of the ultra-stable optical reference cavity, which makes it extremely insensitive to vibrations. The cavity design of low passive acceleration sensitivity combined with a rigid mount allows frequency stable lasers to operate in non-laboratory environments and will be an attractive candidate for transportable optical clock and space applications.