A mathematical model of calculating rotordynamic coefficients associated with leakage steam flow through labyrinth seals was presented. Particular attention was given to incorporating thermal properties of the steam fluid into prediction of leakage flow and subsequent derivation of rotordynamic coefficients, which quantitatively characterize influence of aerodynamic forcing of the leakage steam flow on the rotordynamics. By using perturbation analysis, we determined periodic and analytic solutions of the continuity and circumferential momentum equations for the time-dependent flow induced by non-axisymmetric rotation of the rotor encompassed by a labyrinth seal. Pressure distributions along labyrinth seal cavities and rotordynamic coefficients were compared at the same condition for air and steam flows. Influence of steam flow through the labyrinth seal cavities on rotordynamic coefficients was analyzed in terms of inlet pressure, inlet swirl velocity and rotor speed