An elongate endovascular element for crossing through an obstruction in a blood vessel comprises: a proximal section; a distal tip section of smaller diameter than the proximal section; and a distally-tapering intermediate section extending between the proximal and distal tip sections; wherein the tapered intermediate section has a length that is substantially λ/2 or a multiple of λ/2, where λ is a wavelength of a driving frequency that will produce longitudinal resonance in the element.