Abstarct: Subsonic flows are the major problems in expansion channels of fluid mechanics. They have many applications in diffuser, conversion of piping, heat exchangers, casting, forming and etc. Therefore, in recent decades, many researchers have examined the analytical, experimental and numerical flows. Unlike the previous studies which have been focused on the planar flow in sudden expansions, the flow instability in gradual expansions with different expansion angles is investigated which is the main innovation of current study. In the present study, the ratio expansion 1:3 and extension angles of 30, 45, 60 and 90 degrees is considered. The main goal of this research is to better understand the effects of angles, Reynolds number and Weissenberg number on the structure and flow pattern at different angles. In order to modeling this process in open source software OpenFoam that is toolkit CFD software has used. First of all, the continuity and momentum equations are expressed in Cartesian coordinates and then the general form of fluid viscoelastic structural equation (MPTT model) and viscosity viscometric functions are used. In this study, for explicit discretization of governing equations finite volume method is used. For marching in time, the PISO algorithm is used in the transient state so that the flow parameters in step time have been constant and steady. Furthermore, the time step is increased until convergence of the parameters to be reasonably accurate answers. The accuracy of numerical results is checked baxsed on the results of sudden expansion (at 90 degree). Finally, for a Newtonian fluid flow, all characterized are presented by transverse and longitudinal vortices in the vicinity of the upper and lower walls of the channel on a regular basis. Then the results classified in tables. Also results of numerical investigation for Newtonian fluid and viscoelastic fluid presented like streamline, velocity contour, velocity on the center line. At the final chapter, the results of the survey are presented in detail.