In two recent papers, the authors investigated the bending collapse load of rectangular tubes consisting of a perfectly elastoplastic material. From these investigations, it is found that the collapse may also occur due to the buckling of web in a rectangular tube under bending, when the tube has a cross section with a large aspect ratio of web to flange b/a. In order to evaluate the collapse load of such tubes under bending, the effective width concept given by Rusch and Lindner for a plate compressed with stress gradient was used to calculate the postbuckling strength of the tube web. However, in the solution of Rusch and Lindner, the plate is supported at only one longitudinal edge with the other longitudinal edge being free. This boundary condition is obviously different from that of the tube web. This paper complements the previous work by addressing the postbuckling strength of the web under stress gradients. The postbuckling strength of the web under stress gradients is also calculated using the effective width concept given in AS/NZS 4600 standard and North American specification (NAS) for a plate compressed with stress gradient and supported at both two longitudinal edges. Moreover, the web slenderness also affects the condition for reaching cross-sectional fully plastic yielding when the web is wider. A new method is proposed to predict the maximum moment considering the effect of web slenderness on the cross-sectional fully plastic yielding. The validity of the collapse load estimation is checked by the results of FEM (finite element method) numerical analysis.