This paper performs a theoretical and experimental study of the effect of increasing the velocity of projectiles during the high-speed extrusion of the polyethylene piston through a tapered section (also called a “hydrodynamic” effect). Mathematical modeling is performed using two methods. The first method is a quasi-one-dimensional description of the polyethylene piston deformation on a moving computational grid. The second method is axisymmetric modeling using the ANSYS AUTODYN package. In the experimental studies, the polyethylene piston was preaccelerated using a propellant charge, after which the escape velocity of the projectile was measured. The escape velocity of the projectile after the tapered section increased up to 50% compared to the input velocity. The experimental results are consistent with the theoretical calculations.