In this chapter, we solve the problem of developing a mathematical model for the operation of a two-phase asynchronous automated line, taking into account its structure and the presence of an inter-operational storage device (buffer). First, we’re constructing a system under consideration semi-Markov model with a discrete–continuous phase space of states in the case of the “only via storage device” operating mode. We assume that all system components probability distribution functions are arbitrary. We chose the supporting system to simplify the original model. Then, using the asymptotic phase merging algorithm and the supporting system, we present calculation formulas for the original system’s approximate calculation of stationary reliability characteristics. The results of the chapter open up the possibility of assessing the stationary characteristics of the reliability and efficiency of the system, taking into account the presence of an inter-operational storage device. They allow us to calculate the characteristics using the obtained formulas for any laws of distribution of operating times and restoration of system elements.