Knowledge of the structure of clusters of galaxies is important, since it depends sensitively on the initial density fluctuations and cosmology of the Universe. Cosmological simulations now make clear predictions for the mass profiles of clusters, and it is important to test these in detail. In the context of the CNOC1 cluster survey, redshifts were obtained for galaxies in 16 clusters. The resulting sample is ideally suited for an analysis of the internal velocity and mass distribution of clusters. I will discuss the analysis of this dataset, and will show among other things that the best-fitting models have a mass-density profile that is consistent with the universal dark matter halo profile advocated by Navarro, Frenk & White. We are now following up this work with CFHT weak-lensing observations of the same set of clusters. This will provide further insight into their structure, and may reveal why the results of redshift, weak-lensing and X-ray studies of clusters do not always agree.