This paper examines the robustness of lead time demand models for the continuous review ( r, Q) inventory policy. A number of classic distributions, (e.g. normal, lognormal, gamma, Poisson and negative binomial) as well as distribution selection rules are examined under a wide variety of demand conditions. First, the models are compared to each other by assuming a known demand process and evaluating the errors associated with using a different model. Then, the models are examined using a large sample of simulated demand conditions. Approximation results of inventory performance measures—ready rate, expected number of backorders and on-hand inventory levels are reported. Results indicate that distribution selection rules have great potential for modeling the lead time demand. ►Robustness of lead time demand models is examined for the continuous review ( r , Q ) inventory policy. ►Novel strategies for selecting the most appropriate lead time demand distribution are introduced. ►Analytical and simulation evaluation are performed to examine classic distributions and selection rules. ►We find that distribution selection rules have great potential for modeling the lead time demand.