Schneidmiller, E. Yurkov, M.V. MOC02 electron FEL undulator radiation brilliance 2015 2015-12 Technique of undulator tapering in the post-saturation regime is used at the existing X-ray FELs for increasing the radiation power. We present comprehensive analysis of the problem in the framework of one-dimensional and three-dimensional theory. We find that diffraction effects essentially influence on the choice of the tapering strategy. Our studies resulted in a general law of the undulator tapering for a seeded FEL amplifier as well as for SASE FEL.