The paper deals with mathematical modelling of steady forced bladed disk vibrations and with dynamic stress calculation of the blades. The blades are considered as 1D kontinuum elastic coupled with three-dimensional elastic disk centrally clamped into rotor rotating with constant angular speed. The steady forced vibrations are generated by the aerodynamic forces acting along the blade length. By using modal synthesis method the mathematical model of the rotating bladed disk is condensed to calculate steady vibrations. Dynamic stress analysis of the blades is based on calculation of the time dependent reduced stress in blade cross-sections by using Hubert-Misses-Hencky stress hypothesis. The presented method is applied to real turbomachinery rotor with blades connected on the top with shroud.