A method for calculation of unsteady 3D turbulent flows in hydro turbines of power plants developed for simulation of the transient processes is presented herein. The method is based on joint solution to the Reynolds-averaged Navier-Stokes equations for incompressible fluid flow written for moving mesh, the equation of runner rotation and the system of 1D equations describing propagation of elastic hydraulic shock in the flow domain. The exchange in flow parameters between the penstock and hydro turbine regions is considered in this approach. Results of transient processes simulation are presented for several modes: start-up to the turbine regime, instantaneous load shedding, and output power decrease. Comparison with experimental data is performed.