Abstract: The problem of solving Orr-Sommerfeld equation can usually be transformedinto a complex generalized matrix eigenvalue problem AX=ωBX。 This paper reduces A,Bto upper Hessenberg matrix and upper triangular matrix respectively by U-transformation,then uses Muller′s rootfinding method to obtain all eigenvalues,where the value of charac-teristic polynomial is given by Hyman′s indirect method.When only a judgement of whetherany mode is unstable is needee,the problem can be transformed into a dominant eigenvaluepr...