The subject of this paper is the issue of business continuity and risks of disruptions and the role of insurance. Special importance is given to the problem of supply chain sustainability. The critical element of success in business is maintaining continuous operations. If companies are not in a position to achieve that aim, or to finance their losses after an accident that can cause interruption, they certainly will fail. Insurance has a pivotal role in business and supply chain continuity risk management. As well as in all other cases, insurance cannot directly safeguard companies from accidents and subsequent disruptions but is the most important source of indemnification for losses when insured events materialize. Unlike developed economies, this type of insurance still does not have such importance in Serbia and other former Yugoslavian republics. We conclude that insurance, as an integral part of risk management efforts, should be combined together with other risk management techniques in order to provide business and supply chain continuity.