For a simple graph A = (VA, EA) where VA and EA are the vertex set and the edge set, respectively, the Sigma index of A is defined as  s(A) = Sxy ∈ EA (hx – hy)2, where hx denotes the degree of x ∈ VA.  In order to minimize and maximize the Sigma index among all trees, the extremal trees with fixed degree sequence are described in this study. The properties of the extremal trees are identified.