Traffic congestion in urban road and freeway networks leads to strong degradation of the network infrastructure and accordingly reduced output. Expansion of the available transportation continues to be one of the solution to the increasing traffic congestion, but with destruction of infrastructure.Traffic flow models are studied to be used in transport industry, in ensuring that traffic situations in our roads and highways are managed. Previous studies have modelled traffic flow by Pearson type III distribution and the Inhomogeneous Lighthill, Whitham and Richards Model (LWR) model .Research into application of Poisson to model traffic flow in the Kenyan Context is scanty. Therefore,the study models traffic flow of Thika-Nairobi highway using Poisson distribution model. The study fitted the Poisson model to a weekly traffic flow data obtained by measurement from a point method. The probability of the number of Matatu vehicles passing within the one minute period was varying and depending on the rush hours and normal hours.The parameters of the model were estimated using Analogical and Moments Method using the data from the sample. Based on Chi-square and index of dispersion values the Poisson model was identified as the adequate model for modelling traffic flow of Matatu .The observed data were used to estimate the expected data using the model.Vehicle arrivals can be evaluated by modelling arrival rate in a given interval of time and inter-arrival between the successive arrival of vehicles in a similar way.