The new Medical School of Montpellier, designed by François Fontès, is enclosed by several façades stiffened by the use of glass fins up to 12.71 m high. The main façade assures the monumentality of the institution with its length of more than 60 m. The façade glass panels, with a maximum size of 3.8 × 2.8 m, are stacked transferring the dead load to the bottom panels through plastic setting blocks. The façade panels are fixed with patch-fittings bolted to titanium inserts embedded in the vertical glass fins. The structural system is designed to resist seismic actions and to accommodate the displacement of the main structure under an earthquake scenario. The stability to lateral buckling and under seismic loads is guaranteed by a system of cables and rods which transmits the in-plane forces to the main structure. The post-breakage behaviour of the multilaminate heat-strengthened glass panels and the design of the façade guarantee the stability even under very aggressive accidental scenarios. The paper contains the main issues about the fabrication of titanium inserts laminated with SentryGlas® interlayer. The verification methodology of the glass fin with embedded titanium connections in terms of strength and stability is described. In particular, non-linear buckling analysis J. Torres (B) · N. Guitart · C. Teixidor Bellapart, Les Preses, Spain e-mail: jtorres@bellapart.com N. Guitart e-mail: nguitart@bellapart.com C. Teixidor e-mail: cteixidor@bellapart.com and stability checks based on Eurocodes are proposed. The numerical analyses were completed with pullout tests of aged specimens in order to determine the resistance of the adhesive connections. Finally, a fullscale glass fin was submitted to a three-point bending test to validate the design including the post-breakage behaviour. A brief description of the construction phase is also included.