Recently, a microbial culture device, the morbidostat has been developed to study the evolution of drug resistant microbial population. The operating principle is based on the chemostat with a mechanism that continuously adjusts antibiotic concentration to maintain nearly constant growth inhibition. In a chemostat, nutrient limitation sets the growth rate equal to the dilution rate. In contrast, the growth rate in the morbidostat is set by the level of an inhibitor, such as an antibiotic. In this talk, we present the theoretical analysis for such a device. In particular, we will present the result from a simulation that closely mimics the actual experimental situation with one wild type population and one drug resistant mutant with a control algorithm to continuously adjust the drug concentration. We present the evolution from wild type to drug resistant population over a wide range of parameters such as the mutation rate. The result and the formulation presented here can assist the design of the actual experiment for study of evolutionary pathway to antibiotic drug resistance.