We study modeling for a class of random delay and packet drop channels, that are almost ubiquitous in networked control systems. Such a class of random channels are temporally correlated, assumed to admit a Markovian description in the known literature, and thus the theory of Markov jump linear systems can be applied for design of the stabilizing and optimal or robust controllers. However, why and how such a Markov channel model is derived remained unclear. Based on some simple and reasonable hypothesis on the channel, we show that the class of random delay and packet drop channels can indeed be modeled by finite state discrete Markov chains, thereby enabling application of the theory of Markov jump linear systems to design of the networked control system over such a class of random channels. On the other hand, the channel model presented in this paper differs from the existing one in that it not only includes the derivation of the channel states and transition probability matrix but also mitigates several modeling issues of the existing work, thereby providing a solid footing to the new Markov channel model obtained in this paper.