The buckling collapse of a honeycomb is analyzed in this paper. A novel large-deformation theory using a stiffness method is introduced to compute the collapse surface for a honeycomb under in-plane biaxial stresses. Extensive experiments on a wide range of Nomex honeycombs are reported, and the results compared with the model. The magnitude of the buckling stress depends strongly on the density of the honeycomb and weakly on the shape of the unit hexagonal cell. On the other hand, the shape of the collapse surface depends strongly on the cell geometry and may be thought of as independent of the density of the honeycomb. For honeycombs under out-of-plane loading, readers may refer to the companion paper [1] (Zhang and Ashby, 1992, Int. J. Mech. Sci. 34, 475).