Recently, there has been considerable interest in micro gyroscopes made of silicon chips. It can be applied to many micro-electro-mechanical systems (MEMS): devices for stabilization, general rate control, directional pointing, autopilot systems, and missile control. The mechanical design of the gyroscope is carried out using axiomatic design, followed by the application of the Taguchi robust design method to determine the dimensions of the parts so as to accommodate the dimensional variations during fabrication. Functional requirements are defined twofold. One is the natural frequencies should have fixed values, and the other is the system should be robust to large tolerances. According to the Independence Axiom, design parameters are classified into a few groups. Then, the detailed design process is performed according to the sequence indicated by the design matrix. The dimensions of the structure are determined to have constant values for the difference of frequencies regardless of the tolerances. It is noted that the Taguchi concept is utilized as a unit process of the entire axiomatic approach.