Synchronous lateral vibration is a frequent cause of machine failure and is probably the most common source of machine noise and vibration. Among the broad ranges of faults that cause synchronous vibration, mass unbalance and bow are the most common faults present in the rotor and hence their detailed understanding is required. In the present study, a rotor model having both mass unbalance and bow is analyzed to find the influence of these faults on the synchronous response. The synchronous response of a rotor is a function of influence coefficients due to mass unbalance and bow. The influence coefficients are analytically derived using transfer matrix method for rotor bearing system having both mass unbalance and bow. The correction unbalance vector required to balance the rotor at its first bending critical speed is computed using these analytically derived influence coefficients and the rotor responses measured at a speed much lower than the first bending critical speed. The balancing method needs a good mathematical model for the rotor system in finding the influence coefficients for mass unbalance and bow. This procedure helps in estimating the correction mass in a single trial run and using a single balancing plane, thus reducing the cycle time for balancing flexible rotors. Experiments are carried out on a test rig to verify the procedure. © 2012 The Author(s).