ABSTRACT: Within a certain domain of rock masses, searching all blocks cut by three dimensional stochastic and deterministic discontinuities with finite extensions is a critical basic problem in jointed rock mass researches. This technique is useful for identifying all spatial blocks which locate on the surfaces or within the rock masses and analyzing the procedure of block progressive failure induced by the surface blocks failed. A method called three dimensional block cutting has been developed on the basis of topology and relevant references. The main analysis procedures are given in brief. The method was implemented in programming capable of identifying the spatial blocks and analyzing block progressive failure in relation to slope and underground opening engineering. At last some application cases in practical engineering are shown to demonstrate the usefulness and efficiency of the method and the program. Three dimensional block cutting is an important advancement in block theory and has extensive application prospective in fractured rock masses researches.