This paper presents mechanism and sources of in-phase coupling error (i.e. bias drift) in a micromachined silicon vibratory gyroscope with various vacuum degrees. Based on a detailed analysis of squeeze-film and slide-film dampings acting on each area of the mass and coupling approaches from drive mode to sense mode, the expression of coupling air damping forces were obtained. Another fact causes the drift of in-phase coupling error is, the phase of sense mode varies with the air pressure and can produce error if the demodulation phase is fix. The experiment measuring coupling error has been performed with various vacuum ranging from 7.5 mtorr to 1 atm, which indicated that in-phase coupling force is very limited and can be significantly reduced by lower the air pressure. Comparison of the theoretical and the experimental pressure-bias relation demonstrated that the change of the phase of sense mode is the dominant factor of bias drift with the change of air pressure.