Problems of indentation of orthotropic laminated beams due to flat punches arc solved. Exact solution methods for a subsidiary problem are developed first for both the simply-supported and clamped-ended cases. A numerical iteration algorithm is then employed to assess the possible separation and the real contact area and the contact stresses for a given punch width and a beam span. The contact stresses and separation results for the beams of a typical span reveal various contact conditions that depend only upon the punch width but not the magnitude of the applied load. For a symmetric lamination of the beam, a wide range of punch widths and beam spans are implemented to detect the critical punch widths rendering the onset of separation between the punch and the beam and to establish the threshold curve for the critical aspect ratio of the beam versus the relative punch width. The effects of both the end support condition and slacking sequence of the beam upon the contact and separation scenarios as well as the threshold behavior are thoroughly evaluated.