Though often not explicitly stated, the method of moments is one of the heavily used methods in queueing analysis. By tracing a typical, tagged customer as it proceeds through the system expected values for a wide range of systems, especially single server systems with Poisson arrivals, have been obtained in the last decades. This paper investigates the suitability of the method of moments to derive higher moments. Starting from general considerations, the problems in dealing with higher moments are insulated, and solutions are presented. These results give a deep insight into the nature of the method of moments.