Specifics of emergency development and damage of the pipeline systems network structures at the industrial enterprises are considered. Emergencies in such systems may be associated with the transition to a state of inoperability of a certain set of pipelines (linear elements). If the damage to the pipelines occurs in a random order, such a scenario of events development is called the progressive damage. If the point elements sequentially and randomly transfer to a state of inoperability, then this damage process is called the progressive blocking of transport nodes. The combination of these scenarios of effect on the system in real operating conditions is considered as mixed damage and described using the cyclogram $T(\alpha .\beta )$ . The value $\alpha$ indicates the number of linear elements sequentially damaged, and the value $\beta$ — the number of blocked transport nodes during one exposure cycle. The ability of the system to resist the development of the mixed damage process was assessed using the simulation method by determining the statistical characteristics: the average proportion of the system linear elements; the average proportion of the transport nodes.

The established values of the linear elements average proportion, average proportion of the transport nodes are considered as projections onto the coordinate axes of the vector characterizing the ability of the system to resist the development of the mixed damage. In this case, the large resistance of the system to the development of the mixed damage corresponds to the large values of the vector. It is shown that the comparative assessment of resistance to the mixed damage is allowed only in relation to the comparable network structures. To do so, the analyzed objects should include the same number of nodes, linear elements and consumers of the end product. In addition, the conditions for network structures damage should be similar, i.e. be described by one cyclogram of damage. The examples of solving the problems of the network structures structural synthesis are considered with an assessment of the pipeline systems resistance to the development of the mixed damage process.