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In the last few years, there has been a significant rise in the number of private vehicles ownership, migration of people from rural areas to urban cities, and the rise in the number of under-maintained freeways; all these have added to the perennial problem of traffic congestion. Traffic flow prediction has been recognized as the solution in alleviating and reducing the problem of traffic congestion. In this research, we developed an adaptive neuro-fuzzy inference system trained by particle swarm optimization (ANFIS-PSO) by performing an evaluative performance of the model through traffic flow modelling of vehicles on five freeways ( N 1 , N 3 , N 12 , N 14   and   N 17) using South Africa Transportation System as a case study. Six hundred and fifty (650) traffic data were collected using inductive loop detectors and video cameras from the five freeways. The traffic data used for developing these models comprises traffic volume, traffic density, speed of vehicles, time, and different types of vehicles. The traffic data were divided into 70% and 30% for the training and validation of the model. The model results show a positively correlated optimal performance between the inputs and the output with a regression value R 2   of 0.9978 and 0.9860 for the training and testing. The result of this research shows that the soft computing model ANFIS-PSO used in this research can model vehicular traffic flow on freeways. Furthermore, the evidence from this research suggests that the on-peak and off-peak hours are significant determinants of vehicular traffic flow on freeways. The modelling approach developed in this research will assist urban planners in developing practical ways to tackle traffic congestion and assist motorists and pedestrians in travel behaviour decision-making. Finally, the approach used in this study will assist transportation engineers in making constructive and safety dependent guidelines for drivers and pedestrians on freeways. [ABSTRACT FROM AUTHOR]