Abstract Glass is a widely used engineering material of which the behavior is not well known to the structural engineer and the architect. Its response against working load is also more complex than other materials since it is likely to exhibit considerable nonlinearity that the linear theory does not suffice. Glass wall systems with glass fins placed perpendicularly to the facing glass plates is a widely used structural form for shop fronts as it provides an aesthetic appearance and unobstructed view to the outside environment for the occupants. However, as the load on the fin is in the plane of the plate and along one edge, the glass fin may exhibit lateral instability at the unrestrained edge when under wind pressure. The finite shell element technique is employed for the present study of the strength and stability of the system. Geometrical nonlinearity and failure criterion for brittle materials are used to predict the breaking and buckling load of the system under wind load. To cater for instability and geometrical nonlinearity under wind load, an efficient triangular element suitable for geometrically nonlinear analysis is proposed and adopted. The buckling load of an example glass wall system and the failure load of glass fins with various breadth vs. depth ratio are reported. The trend for the failure load against negative and positive pressure is also shown and tabulated.