In the paper, a calculation method for specifying the centrifugal loads (SCLM) of free turbine rotors (turbine shaft unbalance method) has been put forward. The traditional method does not take this effect into account whereas the unbalance can lead to significant rotor deflections when approaching the critical frequencies. The SCLM in the solution of the problem within the elasticity theory in beam approximation using the finite element method (FEM) and the eigenfunction expansion method was exemplified by a three shaft system. The loads caused by thickness variation, radial runout of outside surfaces and the one of mounting surfaces were considered. An experiment consisting of vibration tests of a gas turbine engine was carried out. The test task showed that taking the shaft unbalance into account gave results being closer to the experimental ones.