For investigating corrugation mechanisms and characterizing sensitive parameters in the metro small curve, a numerical model was established, and the transient dynamics analysis was performed employing the numerical model. Meantime, probability calculations were carried out using Direct Monte Carlo Simulation and Latin Hypercube Sampling, and the sensitivities of random input parameters were analyzed. The results show that the outside wheel-rail contact is in the gauge angle position, while the inside one is in the top-of-rail position. The outside stick-slip distribution is always in the slip state and exhibits multi-point contact; the inside stick-slip distribution exhibits alternating stick-slip and slip states and is all in single-point contact. The formation mechanism of inner rail corrugation can be summarized as the generation of corrugation due to the contact state variation induced by the system instability. The friction coefficient, longitudinal relative slip and modulus of elasticity of the baseplate have greater influence, while the remaining parameters have less effect. Appropriately reducing the friction coefficient, longitudinal relative slip, primary suspension vertical and transverse forces, wheelset transverse displacement and wheel-rail contact angle, increasing the moduli of elasticity and densities of rail pad, baseplate and baseplate pad can make a proactive difference in the corrugation control.