Redistributing the transverse energy flow in the focal plane of a tightly focused radially polarized optical field is described. We develop from theory a generalized analytical model for calculating the distributions of the electromagnetic field and the Poynting vector for a tightly focused radially polarized laser beam superposed with an optical vortex. We further explore the redistribution of the energy flow by designing phase masks, including traditional and annular vortex phase masks. Flexible control of the transverse energy flow rings is obtained with these phase masks. They provide a simple solution to transport absorptive particles along certain paths and therefore might be help in optical tweezer manipulations.