We investigate thermal fluctuations in a smectic A phase of an amphiphile-solvent mixture with molecular-dynamics simulations. We use an idealized model system, where solvent particles are represented by simple beads, and amphiphiles by bead-and-spring tetramers. At a solvent bead fraction of 20% and sufficiently low temperature, the amphiphiles self-assemble into a highly oriented lamellar phase. Our study aims at comparing the structure of this phase with the predictions of the elastic theory of thermally fluctuating fluid membrane stacks [Lei et al., J. Phys. II 5, 1155 (1995)]. We suggest a method which permits to calculate the bending rigidity and compressibility modulus of the lamellar stack from the simulation data. The simulation results are in reasonable agreement with the theory. (C) 2003 American Institute of Physics.