Coaxial gyrotrons offer the potential to generate microwave power in the multi-megawatt levels at frequencies well above 100 GHz 1 , since very high-order volume modes can be used. The presence of the coaxial insert reduces the voltage depression and eliminates the restrictions of mode selectivity, making it possible to maintain the cavity ohmic losses at a reasonable low level (<2kW/cm 2 ) allowing the use of very high-order volume modes.However, the increased beam currents and energies involved can cause loss of stable gyrotron operation by the excitation of spurious high frequency oscillations in the beam tunnel 2-3 . These oscillations seem to be limiting factors for output power and efficiency in several current projects 4 . Specifically, the azimuthally symmetric high-order TE 0n gyro-backward waves are the most dangerous source of parasitic oscillations, since it is difficult to attenuate them 5 .In this work, we perform a parametric study of the geometric properties of the beam tunnel using the space harmonic method (SHM) and the linearized Vlasov equation. The influence of geometry parameters on the growth rate of parasitic oscillations in a simplified coaxial gyrotron beam tunnel is investigated.