The mechanical coupling characteristics of a monolithic tri-axis micro-electromechanical gyroscope have an important effect on the performance of the gyroscope, and the coupling is directly related to the processing error. This paper introduces the structure and principle of a monolithic tri-axis micro-electromechanical gyroscope, establishes a dynamic coupling model, and studies the mechanical coupling problem caused by beam width errors. The finite element analysis tool was used to simulate the harmonic response of the gyroscope structure with beam width error. The driving-to-sensing and sensing-to-sensing coupling characteristics, the equivalent coupling angular rate of the driving mode to each sensing mode, and the cross-coupling coefficients between the sensing modes are investigated. The coupling error under unit beam width error are obtained and can be used as a reference for the structural design of the single-chip tri-axis gyroscope and the precision requirements for processing.