Resilience is one of the key indicators of processing systems, it expresses the behaviour of the system as a result of expected or unexpected failures. This indicator can be essential during systems design and operation, especially, when the system is part of or related to a critical infrastructure. The numerous contributions on systems resilience are related to a wide range of applications, however, there is no general uniform framework for resilience evaluation. For instance, most studies examine resilience as a function of the continuous parameters of the system, usually avoiding the influence of its structure. In the current work, a general framework for determining the structural resilience of processing systems is presented. This framework derives on formulas that satisfy the requirements of the original definition of resilience. The formerly developed P-graph framework is the mathematical basis of the procedure for determining the indicator. The resilience of the system is calculated as a function of the operative subprocesses for all possible failures and is a normalized indicator on [0, 1]. The examination of two industrial case studies shows that the proposed resilience can be an appropriate indicator to be considered in process design.