An improved endoluminal device. The device includes at least a control element (such as a guide wire, tube or related structure) connected to a surrounding sheath and an elastic bias section to control changes to a bias force formed between the control element and the sheath. By applying an external force at a proximal end of the device, the shape can change between varying degrees of deformed shapes and an undeformed shape. In this way, both ease of insertion into the body lumen and anchoring to the lumen is promoted. A distal end of the assembly can be made to change shape for improved steerability, anchoring or both. In a particular form, the anchoring section can work as a floating parachute-like device to pull the assembly by means of the flow in the body lumen, while in a more particular form, the floating parachute-like device may be modified to act as a filter for trapping emboli.