The description and analysis of particle size distributions using log skew Laplace distributions is a new technique designed to overcome various mathematical and computational problems associated with other approaches. This paper presents an application of the method. In particular, it describes fitting log skew Laplace distributions to modern and ancient shoreline sands from Lepcis Magna (near Horns), Tripolitania, with the purpose of discriminating between modern environments and so classifying the ancient samples. Satisfactory discrimination was not always achieved between some of the modern ‘calibration’ shoreline sand samples of known provenance — possibly as a result of the presence of multimodal distributions. One layer in the harbour-infill sequence, previously of unknown provenance, was shown to have collected at, or close to, an ancient shoreline which developed within the ancient harbour. The majority of the ‘ancient’ samples of unknown depositional environments which were excavated from exposures in the Romano-Libyan harbour-infill sands, were shown by this analysis to be of neither beach nor aeolian origin. This conclusion supports field observations which suggested that the greater part of the harbour-infill sequence represented reworked dune palaeosols, developing dune soils and fluvial and lagoonal facies.