Wrapping cape system for removing blocking items from body vessels based on a sheathed bundle of wires and interwoven fibers which is characterized by a configuration comprising the interconnection of a spinal wire, at least one chordal wire, a net, and a pulling string, whereby the spinal wire is stiffer than the chordal wire and one end of the chordal wire is joined with the end-point of the spinal wire, forming a terminal junction, and one end of the pulling string is permanently affixed to an intermediate point of the chordal wire; all constituents are passing through a tubular guide, and are capable of sliding through the tubular guide, as well able to exit from the distal end of the tubular guide; the spinal wire, the chordal wire, and the pulling string, are having their un-joined free ends available for individual handling, directly or indirectly, through the proximal entrance of the said tubular guide; the net is linking the spinal wire and the chordal wire and is contractible-expandable in accordance with the contraction condition that when the spinal wire and the chordal wire are aligned, the net is contracted in one dimension and elongated in the other, thus co-aligned with the spinal and chordal wires (1, 2), whilst when the spinal and chordal wires (1, 2) are in a state of separation the net is expanded and undertaking a two dimensional shape; and where on deployment of the system three actions are performed, namely the wrapping action, the entrapping action, and the tightening action, associated with the performance of a sequence of handling operations involving the application of suitable relative displacements between the tubular guide, the spinal wire, the chordal wire, and the pulling string, as required accordingly, aiming to first capture and then tighten a blocking item trapped in a tubular geometry, with the aid of the accompanying net, whereby: during the wrapping stage, the spinal wire is pulled with respect to the chordal wire in the presence of the surrounding cylindrical geometry, thus imposing the cylindricality constraint upon the expanding part of the assembly, thereby curving the originating profile of the conforming netted chordal wire and forcing it to encircle the contained blocking item, thus wrapping it up to the point where the chordal wire reaches the spinal wire, wherein the chordal wire is adapted to assume a bi-partite helicoidal shape having two branches with opposite spiraling sense; next, during the entrapping stage, pulling string is pulled up until the blocking item is entrapped either by a single conical contraption, or by a conical-and-cylindrical composite formation; subsequently, during the tightening stage, further shrinkage of the net is effected via pulling of the chordal wire with respect to the spinal wire, owing to the built-in contractibility property of the net pattern; thus favorable conditions are established for ultimate removal of the blocking item via total pulling of the whole system, and the system further having - regarding the flexibility of the wires -adaptable softness, in total or in part, uniformly or gradually, either via reduction of their cross-section, globally or locally, and/or via resorting to coiling through spiral winding of the wires, globally or locally, and/or via modification of the mechanical stiffness through thermal and/or chemical treatment of the base material, in conjunction with intentional pretension to predispose the bending of the wires during operation, accomplished either through preparatory mechanical processing and/or via use of special materials, such as shape-memory alloys.