Access to medicines (drugs, diagnostics and vaccines) is essential to promote equitable health care for all though one third of the world’s population does not have access to basic and essential drugs, particularly in the poorest parts of Africa and Asia. In a third world country like India with high industrial capabilities, a large part of the population still lives below the poverty line and there the role of the government becomes crucial in creating the aforesaid access. The chapter deals with three main objectives: (1) to find status of access to free medicine in public secondary hospitals in West Bengal, (2) to identify the factors affecting this access to free medicine and (3) to analyse how this availability of free medicine affects the overall efficiency of these government-run hospitals in West Bengal. For the first purpose, we used descriptive statistics from the secondary data of National Sample Survey Organization (NSSO) and from primary survey on more than 2,000 patients in 86 secondary level hospitals in West Bengal. For the second purpose, we used a multinomial logit regression model. For the third purpose, we used a regression technique to determine what are the barriers of access and how does the efficiency score of hospitals (measured by Data Envelopment Analysis) affect the access to medicine. The chapter concludes that managerial steps should be immediately taken to improve both the quantity and quality of the drugs supplied to these hospitals. Some improvements are also suggested about the prescription system, procurement, storage and distribution system of essential drugs based on some field experience. Need for a modification of the State Essential Drug List is also suggested. © 2015, Springer India.