We study the influence of relativistic rotation on the confinement/deconfinement phase transition in gluodynamics by means of lattice simulations. The simulation is performed in the reference frame which rotates with the system under investigation, where rotation is reduced to external gravitational field. The Polyakov loop and its susceptibility are calculated for various lattice parameters and values of angular velocities which are characteristic for heavy-ion collision experiments. Different types of boundary conditions (open, periodic, Dirichlet) are imposed in directions, orthogonal to rotation axis. It is shown, that the critical temperature of the confinement/deconfinement transition in gluodynamics grows quadratically with increasing angular velocity. This conclusion does not depend on the boundary conditions used in our study and we believe that this is universal property of gluodynamics. We also present first results of the study of the phase diagram of rotating QCD matter with fermions. The results indicate, that effect of the rotation on fermions is opposite to gluons: it leads to the decrease of the critical temperature.