The question of terrorism is becoming a principal problem which influences social safety. Terrorist acts are aimed at frightening people and destabilisation of normal functioning of the state. Terrorists are trying to achieve this goal by bombing civilians and public utility facilities including transport system facilities. One of the elements of a transport system is its infrastructure consisting of roads, railways and bridge facilities. This last element encompasses for example bridges, viaducts, flyovers and culverts. Taking into account the fact that bridge facilities are extremely sensitive to terrorist attacks, the authors of this article decided to focus on them in this study. The work presents an original method of damage risk assessment in engineering facilities in the aspect of potential terrorist attacks. The method is based on two selected multi-criteria optimisation methods. The subject of analyses were four selected bridge facilities. The results of the conducted research and analyses were risk assessments of selected bridges. An advantage of the presented solution is the possibility to justify the adopted hierarchy of decision variants. Using the proposed method one can obtain specific numerical values. They can be used in further analyses conducted on a wider scale and to build a hierarchized database of facilities prone to terrorist attacks.