Multicommodity network flows (MCNF) is a useful tool to solve bandwidth allocation and distribution problems on flows over MPLS (multiprotocol label switching) networks. MPLS has emerged as the protocol of the future due to it's true "multiprotocol architecture" nature, where it use a simple label switching mechanism and provide some level of quality of service (QoS) management features through traffic engineering. The objective of this paper is to propose a model based on multicommodity network flows theory to determine the optimal allocation of flows in a label switched path (LSP) at minimal cost. We discuss implementation issues and present some computational results.