Transporting parcels is an acute problem for the Postal delivery system. It accounts for about forty-five percent of all expenses other than personnel within the Postal System. The vehicle routing problem (VRP) is the problem of finding the optimal routes of delivery or collection from one or several depots to a number of warehouses or customers. In this study, the Nigerian Postal Services mail delivery service was modeled as a VRP using the Abuja Post Office as a case study in order to address the problem of delay in mail delivery occurring frequently in the Nigerian Postal Services. The model developed optimal transportation routes and it is believed that this will find a new way of reducing mail delivery time and at a cheaper transportation cost. The solution entails formulating and solving it as a distance constrained problem (DVRP), formulating and analyzing a Distance-constrained and capacitated Vehicle routing problem (DCVRP). Next, optimal routes were developed for the vehicle routing problem with time windows, (VRPTW), developing and analyzing the optimal routes for the capacitated vehicle routing problem with time windows.