The reliability problem of a network from a source s to some specified terminal points set K (SKT) is discussed. Two gate_varible_reducation principles, algorithms of computing K-trees and minimum K-cuts of a network are proposed firstly. And then using Boolean equations containing gate variables and means of OBDD, an efficient algorithm for computing the K -terminal reliability of a network is also proposed. This algorithm is efficient, as demonstrated by experimental results. This algorithm improves and generalizes the algorithm presented by Rauzy.