In the classic twin design, estimation of genetic and environmental effects is based on the assumption that environmental influences are shared to the same extent by monozygotic and dizygotic twins (equal environment assumption, EEA). We explore the conditions in which the EEA can be tested based on multivariate phenotypic data. We focus on the test whether the correlation between shared environmental factors in dizygotic twins (rC) is less than 1. First, model identification was investigated analytically in Maple and Mx. Second, statistical power was examined in Mx. Third, the amount of bias caused by violation of the EEA was evaluated. Finally, applications to empirical data concern spatial ability in adolescents and aggression in children. Bivariate and trivariate models include several instances in which the EEA can be tested. The number of twin pairs that is needed to detect violation of the EEA with a statistical power of .80 (α = .05) varied between 508 and 3576 pairs for the situations considered. The bias in parameter estimates, given misspecification, ranged from 5% to 34% for additive genetic effects, and from 4% to 34% for shared environmental effects. Estimates of the nonshared environmental effects were not biased. The EEA was not violated for spatial ability or aggression. Multivariate data provide sufficient information to test the validity of the EEA. The number of twin pairs that is needed is no greater than the number typically available in most twin registries. The analysis of spatial ability and aggression indicated no detectable violation of the EEA.