The state 0 of a birth and death process with state space E = {0, 1, 2, ···} is a barrier which can be classified into four kinds: reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier.
