For and , let be the symmetric -stable process on . Denote by the Green function for a bounded open set in . The main purpose of this paper is to show the following upper and lower estimates of for a bounded domain with boundary: There exist constants and depending on , and such that
where . This is first shown by using the explicit expression of the Green function in the case that is the ball of center 0 and radius and then it is used to get the result for general bounded domains. Some approach is taken from Z. Zhao [J. Math. Anal. Appl. 116, 309-334 (1986; Zbl 0608.35012)] in which Brownian motion case is concerned. Hence the essential change of the proof is necessary according to the jumping property of the sample paths. As applications, 3G Theorem and the estimates of the mean exit times are given.