The flow behavior of polystyrenes is investigated numerically for a cross-slot geometry using Rolie-Poly model with finite extensibility, and governing equations for the polystyrene melts are solved by finite volume method with domain extension technique on the collocated grid. The effect of molecular weight, flow rate, and two kinds of Weissenberg numbers on the principal stress difference (PSD) profiles are discussed detailedly. The microstructures of polymer melts, including molecular orientation, extension, and deformation, are also investigated and presented in this paper. We found that the orientation of Weissenberg number is the major factor affecting the PSD profiles and the performance of the Rolie-Poly model has been improved greatly by introducing finite extensibility at high extension rate. The numerical results are consistent with the available experiment results, which demonstrate the capabilities of single-mode Rolie-Poly model with finite extensibility to simulate the flow behavior of polystyrenes and the numerical method developed in this paper.