The emergence of antibiotic-resistant strains of bacteria has been increasing to become one of the most serious problems of Public Health. The increase in treatment with these drugs and their inappropriate use are main cause of this emergency. Recently, scientific community has become clear that, a better understanding of the dierent mechanisms of acquisition of bacterial resistance have great importance in preventing infection and development more eective antibiotics. In this work, we consider bacterial resistance adquisition by mutation due to antibiotic exposure. We formulated a mathematical model describing the interaction between sensitive and resistant bacteria to an antibiotic. Analysis qualitative reveals the existence of a free-bacteria equilibrium, resistant-bacteria equilibrium and an endemic equilibrium where both bacteria coexist sensitive and resistant bacteria.