The subject of this invention is in the field of medicine, particularly surgery, and is intended for the treatment of benign tumors and angiomas. A hemangioma is an angioma, or tumor, formed by an anomalous proliferation of vascular endothelium, forming an undesirable mass, which can occur anywhere in the body. The resulting disease is known as hemangiomatosis. The method of this invention is comprised of a reduction of the arterial blood flow to the hemangioma which limits the blood circulation in the tumor mass, thus creating favorable conditions for subsequent ferromagnetic embolization from externally and selectively applied electromagnetic or ultrasound energy and sclerotization of the tumor tissue, preventing the spread of ferromagnetic particles through the vessels and into other organs and systems. At the same time, maintaining the blood flow, though reduced, prevents the development of a total necrosis due to acute impairment of the tumor's blood circulation, which significantly reduces the general toxic effect. The reduced blood stream still leaves the possibility of introducing medication into the tumor, which reduces the possibility of complications during the postembolization period.