Measurement and modelling of distributions of data communication times is commonly done for telecommunication networks, but this has not previously been done for message passing communications on parallel computers. We have used the MPIBench program to measure distributions of point-to-point MPI communication times for two different parallel computers, with a low-end Ethernet network and a high-end Quadrics network respectively. Here we present and discuss the results of efforts to fit the measured distributions with standard probability distribution functions such as exponential, lognormal, Erlang, gamma, Pearson 5 and Weibull distributions.