The present invention relates to apparatus for cutting out a human or animal tissue, such as a cornea, or a lens, said apparatus including a treatment device for producing a pattern consisting of at least two impact points in a focusing plane from a L.A.S.E.R. beam generated by a femtosecond laser (1), the treatment device being positioned downstream from said femtosecond laser, remarkable in that the treatment device comprises an optical focusing system (5) for focusing the L.A.S.E.R. beam in a cutting-out plane, and a control unit (6) able to control the displacement of the optical focusing system along an optical path of the L.A.S.E.R. beam for displacing the focusing plane in at least three respective cutting-out planes so as to form a stack of surfaces for cutting out the tissue.