We reproduce the symmetric and asymmetric "rippled" P(beta') states of lipid membranes by Monte Carlo simulations of a coarse-grained molecular model for lipid-solvent mixtures. The structure and properties compare favorably with experiments. The asymmetric ripple state is characterized by a periodic array of fully interdigitated "defect" lines. The symmetric ripple state maintains a bilayer structure, but is otherwise structurally similar. The main force driving the formation of both ripple states is the propensity of lipid molecules with large head groups to exhibit splay.