Abstract: Sombor index is a new chemical topological index introduced based on vertex degree.The Sombor index of two finite simple connected graphs is studied after five graph operations（i.e.,connection operation,Cartesian product operation,crown operation,dictionary order product operation,and symmetric difference operation）,and their extremal graphs are described.Firstly,the edges of the expressions after each operation are classified.Then a valuation inequality for the upper bound of the Sombor index of the graphs of each operation is given by using the maximum degree of the vertices and the inequality deflation.Finally,the condition of obtaining the upper bound of Sombor index is given to be that both graphs are regular graphs.