A mathematical model for the interaction of bacteria and bacteriophage incorporating the bacterial mutation has been proposed and analysed in this chapter. We assume that the mutant bacteria are formed when the susceptible bacteria interact with the bacteriophage. The bacteriophage, when it interacts with susceptible bacteria, results in the production of infected bacteria which in turn produces so many phages into the system. The proposed model has been analysed with local stability theory and Hartman–Grobman theorem at the various equilibrium points. A simple Hopf bifurcation has been discussed to explore the stable limit cycle in the system.