Eulerian hydrocode simulations using the Mechanical Threshold Stress (MTS), Zerilli-Armstrong (Z-A), and Johnson Cook (J-C) flow stress models were performed to provide insights into dynamic tensile extrusion (DTE) experiments with copper (Cu) and tantalum (Ta). The extrusion of Cu and Ta projectiles was simulated with an explicit, two-dimensional Eulerian continuum mechanics hydrocode and compared with data to determine if this extrusion concept is a useful indirect hydrocode material strength model evaluation experiment. The data consisted of high-speed images of the extrusion process, photon Doppler velocimetry (PDV) to measure the projectile velocity history and die transit time, dynamic temperature measurements of the extruded material, recovered extruded samples, and post-test metallography. The hydrocode was developed to predict large-strain and high-strain-rate loading problems. The code features a high-order advection algorithm, material interface tracking scheme, and van Leer monotonic advection-limiting algorithm. The strength models were utilized to evolve the flow stress (σ) as a function of strain, strain rate, and temperature. Average strain rates on the order of 104 s−1 and plastic strains exceeding 300% were predicted in the extrusion of copper at impact velocities between 400–450 m/s, while plastic strains exceeding 800% were predicted for Ta. The predicted and measured deformation topologies, projectile velocity profiles and die transits times, plastic strains, and temperatures were qualitatively compared. The flow stress distributions predicted by the three strength models were also compared for one experiment. Finally, the feasibility of using DTE to evaluate hydrocode strength models will be discussed.