Abstract.To meet the needs of the joint operation under the uncertain information conditions, the description and effectiveness of weapon system-of-systems combat networks has been widely researched. The Timed influence nets(TIN) is an useful tool to describe the uncertain causal relations in the weapon system-of-systems combat networks and has been used for the effectiveness evaluation in alternative military actions. However the uncertain time delay effect is not well considered and computed in the TIN. In this paper, the Random Timed Influence Nets(RTIN) is proposed to introduce the random time delay in the TIN. First, it is introduced that the basic concepts and algorithms used in the RTIN model including the time delay parameter, the belief sequence and the belief-spread algorithm. And then an instance is given in this paper to demonstrate the RTIN modeling process and the result of effectiveness evaluation using the belief spread algorithm.