The specifics of the pipeline systems operation at the development of process of structural elements damage are considered in the article. Blocking of the transport node is called the damage, at which further delivery of the end product through this node becomes impossible. Such an event is equivalent to the simultaneous transition to the state of inoperability of all the pipelines converging in this node. If the nodes of the transport system are blocked sequentially and in random order, then the specified scenario of the development of an emergency situation is considered as a progressive blocking. If during this process the possibilities of intrasystem redistribution of transport flows appear to be exhausted, so some part of it and then all the consumers of the end product are disconnected from the source.
The characteristic of the progressive interlock process is the indicator of Fx durability, which represents the average proportion of the system nodes, the sequential blocking of which in random order results in disconnection from the source of all the end product consumers. For the given network structure, the Fx value is set using the method of simulated computer modelling. The network structures with the «tree» topology are considered, and the assessment is provided for their resistance to progressive blocking. It is shown that such systems are characterized by low ability to resist the development of this process. It is possible to increase the resistance of the systems to damage due to inclusion of backup linear elements in their composition, connecting the end products consumers between each other. The greatest positive effect is achieved when a clique is formed as a part of network structure, i.e. full subgraph, the number of which nodes corresponds to the number of the end product consumers.
It was established that the process of progressive blocking of transport nodes is rather destructive in relation to the existing pipeline systems, therefore, the ability to resist its development through structural transformations of the system is limited.