Two kinds of practical approximate simulation methods for three-dimensional viscoelastic flow in a die have been developed by which solutions at high shear rate can be obtained with low memory capacity and CPU time. The velocity and stress fields were calculated separately. The velocity field was obtained using the pure-viscous non-Newtonian model and the stress field using the viscoelastic model by substituting this velocity field. In one case the White-Metzner model was applied as a viscoelastic model without a square term in stress. In the second case the stress field was calculated by the streamwise integration which could apply even to the viscoelastic model including the square of stress. In addition a modified pure-viscous non-Newtonian model has been developed respresenting the strain-thickening elongational viscosity in order to extend these approximate methods to similar materials. The velocity field which was calculated using a modified pure-viscous non-Newtonian model was considerably closer to that for the viscoelastic model with the same flow characteristics as shown for the original pure-viscous non-Newtonian model.