A unified treatment is presented of two well-known problems which have until now been considered separately. The two problems are: (a) the linear problem of pure bending of curved tubes, and (b) the nonlinear problem of pure bending of straight tubes. In both problems the effect of uniform internal pressure is included. The essential step in the present analysis is the treatment of the flattening of the cross sections of the tube by means of a theory of finite bending of circular rings. The general results of the paper are used to obtain improved values for the stability parameters in the problem of flattening instability of originally straight tubes acted upon by end bending moments, and also to obtain results on the effect of slight original curvature of the beam axis in the problem of flattening instability.