This article describes a new model of a cooperative file sharing system in a wireless Mesh network. The authors approach is to develop an efficient and cooperative file sharing mechanism based on opportunistic random linear Network Coding. Within this mechanism, every node transmits random linear combination of its packets according to cooperative priority, which is computed in a distributed manner according to the node-possible contribution to its neighbor nodes. With this mechanism, the more a node contributes to others, the more the node has chances to recover the entire file first. The performance metrics of interest here are: the delay until all the packets in a file have been delivered to all nodes, and an ideal packet size, by the use of which the authors can get the minimum transmission delay. Through extensive simulation the authors compare their mechanism with the current transmission process in a wireless Mesh network without random linear Network Coding. The authors found that using their mechanism, the nodes can cooperatively share the entire file with less transmission time and delay than the current transmission process without random linear network.