FIELD: medicine.SUBSTANCE: group of inventions relates to medicine and medical equipment, in particular to method of connecting mechanical connecting unit of laser device to stabilising component held on biological tissue by its suction force, and to apparatus for cutting part of eye by means of focused laser irradiation. Method lies in the following: mutual approaching of connecting unit and stabilising component is carried out until first relative position, in which any contact between tissue and surface adjacent to it is absent or already exists, is achieved. After that, with said components being in said first relative position, pumping out of sucking chamber, formed between connecting unit, stabilising component and tissue surface, is performed in order to create contact between tissue and adjacent to it surface of connecting unit or for increasing zone of already existing contact. Claimed apparatus for cutting tissue of part of eye by means of focused laser irradiation, in particular with application of method described above, contains unit of adhering by suction ring, intended for installation on eye and having ring axis, mechanical connecting unit, made separately from unit of adhering by suction ring with possibility of its travel along ring axis until connection by creation of contact, to unit of adhering by suction ring and provided with contact glass for giving eye surface required shape, means for pumping out for performing pumping out of first suction chamber, limited by unit of adhering by suction ring, connecting unit and eye surface, sensor means for detecting achievement by connecting unit and unit of adhering by suction ring of first relative position along said axis, in which any contact between tissue and surface adjacent to it is absent or already exists. Apparatus also includes control device, connected with sensor means and with means for pumping out, adjusted to ensuring initiation of pumping out first suction chamber as response to detectio
