Abstract: Numerical oscillation always occurs when the standard Galerkin method is applied to the pure convection coupled piping model, and it affects the calculation quality and efficiency seriously. The characteristics of piping governing differential equations and the applicability of the standard Galerkin method are analyzed, with the results showing that the nonlinear convection item in the governing differential equations induces the non-self-adjoint equations and unsymmetrical total matrix, and that the optimal approximation character of the standard Galerkin method is destroyed, resulting in the numerical oscillation. The stabilized finite element technique, Streamline Upwind Petrov/Galerkin (SUPG), is employed to improve the coupled piping mathematical model. The results indicate that the SUPG method can eliminate numerical oscillation of pure convection equations effectively, and gain more satisfactory results under the condition of fewer elements compared with the standard Galerkin method.