The use of inflatable structures for space missions is at an ever demanding increase. The advantages of such structures include easy assembly and low launch weight. To consider using inflated cylindrical beams as support booms in aerospace applications, an accurate and efficient method of structural analysis must be developed. In the present paper, we investigate the buckling of a pre-inflated cylindrical membrane shell of isotropic elastic material subjected to bending, ignoring any warping effects of the beam. We will however consider the non-linear pre-buckled ovalisation of the beam. Once the beam has reached its final buckled state, an internal inflation pressure is applied to the cylindrical membrane beam to restore it to its initial configuration. For comparison purposes, a hyper-elastic model simulated in Abaqus FEA Software is also considered. From the bifurcation on the pre-buckled state to the uniform wrinkling state is investigated through an eigenvalue analysis. The values of the bifurcation moment and curvature of the beam are also calculated and a comparison is made with analytical predictions. For a wide range of thickness-to-radius ratio values, the effects of the cylindrical post-inflation on the bifurcation moment, critical wavelength and the corresponding curvature are also investigated.