The present invention is directed to a dilator having a stiffened shaft for use as part of an introducer sheath assembly. The dilator includes a stiffener tube and a tip of the dilator which extends distally to the dilator stiffener tube. The transition between the stiffener tube and the tip of the dilator is positioned such that when the dilator is positioned within the catheter sheath, the transition is also positioned within the catheter sheath. By positioning the transition between the stiffener tube of the dilator and the tip of the dilator inside the catheter sheath, the catheter sheath can provide strain relief subsequent to lateral movement of the tip of the dilator in a manner that can prevent kinking of the dilator tip at the transition between the stiffener tip and the tip of the dilator.