The College of Science in the Department of Mathematics discussed a master's thesis entitled Numerical Study of the Start-Up of Inelastic Fluid Flows Through a Channel:  Finite Element Method for postgraduate student Ahned Jameel Ganem. This thesis simulates inelastic fluid flow through an axisymmetric rectangular channel, considering shear and extensional viscous models. Navier-Stokes and continuity equations in cylindrical coordinates govern the fluid's behavior. The fluid's viscosity varies with shear or strain rate. Two constitutive inelastic models are presented for this problem. The initial task utilizes a shear-thinning, shear-inelastic model (SI-Fit-I) to account for viscosity.