Recently, Elias et al. (Science 323, 610 (2009).) reported the experimental realization of the formation of graphane from hydrogenation of graphene membranes under cold plasma exposure. In graphane, the carbon-carbon bonds are in sp3 configuration, as opposed to the sp2 hybridization of graphene, and the C–H bonds exhibit an alternating pattern (up and down with relation to the plane defined by the carbon atoms). In this work we have investigated, using reactive molecular dynamics simulations, the role of H frustration (breaking the H atoms up and down alternating pattern) in graphane-like structures. Our results show that a significant percentage of uncorrelated H frustrated domains are formed in the early stages of the hydrogenation process, leading to membrane shrinkage and extensive membrane corrugations. This might explain the significant broad distribution of values of lattice parameter experimentally observed. For comparison purposes we have also analyzed fluorinated graphane-like structures. Our results show that similarly to H, F atoms also create significant uncorrelated frustrated domains on graphene membranes.