In biomedical research there is a growing interest in the use of hierarchical Poisson regression models. Although sample size calculations for testing parameters in a Poisson regression model with prespecified power and size have been previously done, very little attention has been paid to this problem for the hierarchical model. We propose to use Monte Carlo simulations to calculate the sample size necessary for the Wald test. The effect of the number of clusters and the covariance structure of the fixed effects is also studied in a simulation study. The method and the simulation study are also extended to the case of the hierarchical Zero-inflated Poisson regression model in order to obtain analogous results there.