Several association studies support the hypothesis that genetic variants can modify the influence of environmental factors on behavioral outcomes, i.e., G x E interaction. The case-control design used in these studies is powerful, but population stratification with respect to allele frequencies can give rise to false positive or false negative associations. Stratification with respect to the environmental factors can lead to false positives or false negatives with respect to environmental main effects and G x E interaction effects as well. Here we present a model based on Fulker et al. (1999) and Purcell (2002) for the study of G x E interaction in family-based association designs, in which the effects of stratification can be controlled. Simulations illustrate the power to detect genetic and environmental main effects, and G x E interaction effects for the sib pair design. The power to detect interaction was studied in eight different situations, both with and without the presence of population stratification, and for categorical and continuous environmental factors. Results show that the power to detect genetic and environmental main effects, and G x E interaction effects, depends on the allele frequencies and the distribution of the environmental moderator. Admixture effects of realistic effect size lead only to very small stratification effects in the G x E component, so impractically large numbers of sib pairs are required to detect such stratification.