A nascent ridesharing industry is being enabled by new communication technologies and motivated by the many possible benefits, such as reduction in travel cost, pollution, and congestion. Understanding the complex relations between ridesharing and traffic congestion is a critical step in the evaluation of a ridesharing enterprise or of the convenience of regulatory policies or incentives to promote ridesharing. In this work, we propose a new traffic assignment model that explicitly represents ridesharing as a mode of transportation. The objective is to analyze how ridesharing impacts traffic congestion, how people can be motivated to participate in ridesharing, and, conversely, how congestion influences ridesharing, including ridesharing prices and the number of drivers and passengers. This model is built by combining a ridesharing market model with a classic elastic demand Wardrop traffic equilibrium model. Our computational results show that (i) the ridesharing base price influences the congestion level, (ii) within a certain price range, an increase in price may reduce the traffic congestion, and (iii) the utilization of ridesharing increases as the congestion increases. Copyright (c) 2014 John Wiley & Sons, Ltd.