Various numerical methods are available to compute the transient response of flexible rotor-bearing systems, subjected to a sudden change in imbalance. The procedures in use are capable of predicting the response of linear as well as nonlinear systems. In general, the transient response of rotor-bearing systems can be obtained by using the methodology of finite elements combined with a numerical integration scheme. The methods of integration commonly used are model superposition, time-marching schemes, and transfer matrix methods. The discrete model is integrated forward in time to generate a transient dynamic response. These methods generally involve a large number of calculations which is computationally very costly especially when dealing with large degrees-of-freedom systems. A new method has been introduced for performing a nonlinear transient domain analysis of flexible rotorbearing systems, operating under simulated blade loss conditions. The proposed method is demonstrated to be computationally more efficient than existing methods and ideally suited to the simulation of flexible rotorbearing systems.