Problems of secure communication and computation have been studied extensively in network models, for example, Franklin and Yung have studied secure communications in the general networks modeled by hypergraphs. Radio networks have received special attention in recent years. For example, the Bluetooth and IEEE 802.11 networks are all based on radio network technologies. In this paper, we use directed colored-edge multigraphs to model the radio networks and study reliable and private message transmissions in radio networks.