A rotational symmetry finite element model is provided to calculate gas turbine shaft critical speeds and unbalance response analysis.A Fourier series representation allows the three-dimensional shaft geometry to be modeled in a basic section by using three-dimensional element.Unlike a beam element model

a solid element representation allows the actual rotor geometry to be modeled.A matrix reduction technique is used to reduce the degrees of freedom.An engineering example of marine gas turbine rotor is applied to the verification of the provided model.