We consider continuous review perishable inventory models with renewal batch demands. Assuming zero lead time, we construct an embedded Markov chain. With a probabilistic approach, we derive a closed-form long run average cost function under the (s,S) replenishment policy. Numerical analysis is then used to identify the properties of the cost function and to demonstrate the impacts of changing batch sizes and other system parameters. Based on these results, a heuristic approach to handle problems with positive lead times is proposed. The performance of the heuristics against simulation results demonstrates its effectiveness and accuracy.