Based on the theory of friction self-excited vibration and the measured data of rail corrugation, the cause of rail corrugation in metro straight section was analyzed. Then, using the stochastic finite element method, the sensitivity of each parameter to rail corrugation was studied by selecting the elastic modulus E1 and density ρ1 of the wheel-rail material, the elastic modulus E2 and density ρ2 of the track slab material, the wheel-rail coefficient of friction f, the fastener vertical stiffness K and vertical damping C, the wheel-rail longitudinal relative slip s as the random parameters. The results show that under the support of Cologne egg fastener track, the characteristic frequency of friction self-excited vibration of wheel-rail system is close to the characteristic frequency of measured corrugation, indicating that the occurrence of rail corrugation is related to the friction self-excited vibration of wheel-rail system under the condition of saturated creep force. The parameter sensitivity analysis illustrates that the influence degree of each random parameter on the real part αi of complex eigenvalue is E1>ρ1>C>E2>ρ2>f>K>s in turn. E1, C and s are positively correlated with the real part αi of complex eigenvalue, while the remaining 5 parameters are negatively correlated with the real part αi of complex eigenvalue. Therefore, appropriate decrease of E1, C and s, and increase of ρ1, E2, ρ2, f and K can play a positive role in the control of rail corrugation.