Many practical arc routing problems involve finding paths or tours that traverse a set of arcs in a graph. The aim of solving such problems is to determine a least cost tour which covers all or subset of arcs in a graph with or without constraints. The Rural Postman Problem (RPP) is one of the most central problem in arc routing. In a daily life, RPP is applied many practices like delivering, road maintenance, electric meters reading, security patrols travelling and snow plowing operations to determine optimum vehicle routes. Waste collection operations also can be modeled as a RPP. The wastes are in small containers located almost continuously along streets in the centres of the cities. In this study, The RPP approach has been addressed and the mathematical formulation is used for determining optimum route of waste collection vehicle that travelling the streets for collection garbages in the city of Erzurum in Turkey. The model is conducted on the networks which have been created for different areas of the city of Erzurum and the results are given.