The force needed to buckle a thin elastic surface is proportional to its bending rigidity. This fact suggests using a buckling setup to measure the bending modulus of lipid membranes. Extending the work of Noguchi [Phys. Rev. E 83, 061919 (2011)], we systematically derive highly accurate analytical expressions for the forces along and perpendicular to the buckle, and we elucidate some of their ...