Random effects models for hierarchically dependent data, e.g. clustered data, are widely used. A popular bootstrap method for such data is the parametric bootstrap based on the same random effects model as that used in inference. However, it is hard to justify this type of bootstrap when this model is known to be an approximation. In this paper we describe a random effect block bootstrap approach for clustered data that is simple to implement, free of both the distribution and the dependence assumptions of the parametric bootstrap and is consistent when the mixed model assumptions are valid. Results based on Monte Carlo simulation show that the proposed method seems robust to failure of the dependence assumptions of the assumed mixed model. An application to a realistic environmental data set indicates that the method produces sensible results. Supplemental materials for the article, including the data used for the application, are available online.