An analytical model is presented to simulate the effects of tooth backlash and sleeve bearing clearance on the vibration spectra of high‐speed spur gear boxes. Elasticity in bending and torsion of the shafts, time‐varying mesh stiffness, tooth backlash, and Hertzian mesh damping, friction between engaged teeth, and interaction between gear box casing and internals are accounted for. During contact between journal and bearing, where time‐varying contact stiffness with consideration of damping at contact point is accounted for, bearing clearance, system vibration, and bearing forces are calculated. The analysis is applied to a single stage gear box and equations of motion are numerically integrated to obtain system response in the time domain. The response is transformed into frequency domain using a fast Fourier transform (FFT) algorithm and samples of the results are shown for different values of backlash and bearing clearance.