Abstract: This paper introduces some basic properties on epimorphic polynomial.And it is concluded that if ｎ≥５ then for any  Ｓ０Zwith ｜Ｓ０｜＝ｎ，Ｅ（Ｓ０，Ｔ０）＝.Furthermore,a method of  constructing some irreducible polynomials in Ｚ[ｘ] is obtained:suppose　φ（ｘ）∈Z[ｘ] with degree≥5 and all its roots are different integral from each other,ｆ（φ（ｘ））  is irreducible on Q when　ｆ（ｘ）∈Z[ｘ] is irreducible on Q with degree equals 2.

Key words: epimorphic polynomial, irreducible, integral ring