Viscoelastic fluids, which are often found in synthetic resins, exhibit Barus effects and shear thinning. The Barus effect is a phenomenon that occurs when fluid is jetted out of a narrow tube(die) and expands at the outlet. Shear thinning is derived from the property that the viscosity decreases at high shear rates. The purpose of this study is to reproduce these phenomena on a computer by introducing the Giesekus model into the moving surface mesh-incorporated particle method. As for the calculation results, the velocity distribution of the Poiseuille flow was consistent with the theoretical solution, and shear thinning was properly expressed. The expansion diameter ratio of the spouting flow from a die had the similar large/small relationship as in the past papers.