Helfrich's theory predicts that the bending free energy of a tensionless amphiphilic bilayer is proportional to the square of the Fourier coefficients of the undulation modes. Equilibrium molecular dynamics simulations with coarse-grained amphiphiles confirm the correctness of this prediction for thermally excited undulations. The proportionality constant then provides the bending rigidity of the layer. Non-equilibrium methods, in particular umbrella sampling, potential of mean constraint force, and thermodynamic integration in Cartesian coordinates, have been used to extend the range of sampled amplitudes. For small amplitudes there is a good agreement with the equilibrium simulations, while beyond the thermally accessible amplitudes a clear deviation from theory is observed. Calculations of the elastic modulus showed a pronounced system size dependence. (C) 2003 American Institute of Physics.