Cavities initially in weak coherent states are considered. The entanglement tensor approach is used to quantify the degree of entanglement. The tripartite entanglement dynamics of the system comprising three twolevel atoms resonantly interacting with three cavities coupled by two optical fibers is studied. The influence of cavity-fiber coupling constant on the tripartite entanglement among atoms and the influence of intensity of the cavity field on that are discussed. The tripartite entanglement among atoms is weakened with coupling constant between cavity and fiber increasing. On the other hand, it is strengthened with intensity of the cavity field increasing.