An intracorporeal device, preferably a guidewire, and method of making same that has an elongate inner core element with an outer layer of material disposed about the core element. The layer of material can be applied as a braid, strand or smooth layer of material, and is preferably a metal. If the layer of material is applied as a braid or strand, it may be subsequently cold drawn so as to create a smooth layer from the braid or strand. The inner core element may be homogeneous, or may consist of drawn filled tubing with at least two layers of material, preferably biocompatible metals. In this way, the multiple layer distal section of the elongate core can be shaped or ground so as to achieve the desired mechanical properties and provide surfaces for attachment of components that are readily bonded or soldered to.