The control of highly infectious diseases of livestock such as classical swine fever, foot-and-mouth disease, and avian influenza is fraught with ethical, economic, and public health dilemmas. Attempts to control outbreaks of these pathogens rely on massive culling of infected farms, and farms deemed to be at risk of infection. Conventional approaches usually involve the preventive culling of all farms within a certain radius of an infected farm. Here we propose a novel culling strategy that is based on the idea that farms that have the highest expected number of secondary infections should be culled first. We show that, in comparison with conventional approaches (ring culling), our new method of risk based culling can reduce the total number of farms that need to be culled, the number of culled infected farms (and thus the expected number of human infections in case of a zoonosis), and the duration of the epidemic. Our novel risk based culling strategy requires three pieces of information, viz. the location of all farms in the area at risk, the moments when infected farms are detected, and an estimate of the distance-dependent probability of transmission.