Material handling is one of the most important issues that should be taken into account for eliminating waste and reducing the cost. It is one of the seven wastes defined in the concept of lean manufacturing. In this study, for a lean material handling system under the lean manufacturing conditions such as pull-based and repetitive manufacturing, a system consisting of periodically moving vehicles in certain routes is taken into consideration. This system is also called milk-run distribution system. Application of milk-run distribution systems in plants standardizes the material handling system and eliminates the waste. Although there are huge numbers of studies related with inbound and outbound logistics, there are few studies especially related with milk-run applications in the manufacturing area. Within this study, based on the observations in real manufacturing environment and limited literature, the milk-run distribution problem in the plants is categorized and explained. For one of the main categories, modeling is performed. The objective of the developed models is to minimize the number of vehicles and the distance traversed. A numerical example inspired by real applications is presented for showing the applicability of the developed models.