This paper is based on data obtained from most recent transportation studies done in the Metropolitan Area of Valle de Aburrá, city of Medellín and other 9 municipalities. The studies were based on an Origin/Destination Survey (2005), Analysis of bus routes (2006), and Mobility Master Plan (2006). This paper explains the process of writing a software application for a given network (Network of Medellin) that solves the deterministic user equilibrium problem. The software code was implemented in Visual Basic .NET®,supported by some operations using Microsoft Excel®, and hardcoded for a segment of the Medellin network. The user equilibrium distribution of flow was found by using the Frank-Wolfe algorithm. The applied algorithm was analyzed in some aspects such as number of iterations, convergence patterns, response time, as well as changes in network demand. The traffic assignment models were analyzed by using the algorithm during the P.M. peak hour (hour of highest traffic congestion). The analysis was compared with the resultsfrom the traffic assignment procedure using TransCAD® (well-known and used transportation demand software) for the 2005 database and it was found that the software is somewhat faster than the algorithm, but the latter could be a good tool for practitioners and students for modeling small networks.