Composite thermoplastic materials, like glass fiber reforced polypropropylene, are used increasingly in several industries. In particular, glass fiber reinforcement is used to improve the mechanical properties of thermoplastics, due to the high fiber modulous and to the better adesion between the fibers and the polymeric matrix. However, few data of material properties of these fluids are avaiable in the literature. In this work, a study of shear and elongational properties of a commercial short glass fiber reinforced polypropylene is presented. The shear and elongational viscosities were obtained using the pressure drop measured at a capillary rheometer, with axisymmetric converging dies. Two different die geometries were used: semihyperbolically convergent dies and conical convergent dies. In the last case, the elongational viscosity was obtained using the Cogswell and Binding analysis. Numerical simulations were also performed, to investigate the flow field through the extrusion die process, and to evaluate the pressure drop and elongational viscosity. The conservation equations of mass and momentum were solved via the finite element method, using the commercial program POLYFLOW (Ansys). The Maxwell, Oldroyd B and Phan Thien-Tanner (PTT) constitutive equations were used to model the viscoelastic mechanical behavior of Polypropylene, but the comparison between numerical results and experimental data obtained from the capillary rheometer did not show good agreement.