An atherectomy system for coring, ingesting and removing an obstruction from within a patient's vessel, comprising a flexible guide-wire insertable into the vessel, a flexible rotary-catheter being rotatably disposed and insertable into the vessel over the flexible guide-wire, having a rotary coring device, at its distal end for making a peripheral cut in an obstruction located in front of it, relative motion between the flexible rotary-catheter and the flexible guide-wire is used to mechanically enable the ingested obstruction material to proximally move into the flexible rotary-catheter.