The developing steady flow of Oldroyd-B and Phan-Thien-Tanner (PTT) fluids through a two-dimensional rectangular channel is investigated computationally by means of a finite volume technique incorporating uniform collocated grids. A second-order central difference scheme is employed to handle convective terms in the momentum equation, while viscoelastic stresses are approximated by a third-order accurate quadratic upstream interpolation for convective kinematics (QUICK) scheme. Momentum interpolation method (MIM) is used to evaluate both cell face velocities and coefficients appearing in the stress equations. Coupled mass and momentum conservation equations are then solved through an iterative semi-implicit method for pressure-linked equation (SIMPLE) algorithm. The entry length over which flow becomes fully developed is determined by considering gradients of velocity, normal and shear stress components, and pressure in the axial direction. The effects of the mesh refinement, inlet boundary conditions, constitutive equation parameters, and Reynolds number on the entry length are presented.