Parallel and distributed systems may operate in an environment that undergoes unpredictable changes causing certain system performance features to degrade. Such systems need robustness to guarantee limited degradation despite fluctuations in the behavior of its component parts or environment. This research investigates the robustness of an allocation of resources to tasks in parallel and distributed systems. The main contributions of this paper are (1) a mathematical description of a metric for the robustness of a resource allocation with respect to desired system performance features against perturbations in system and environmental conditions, and (2) a procedure for deriving a robustness metric for an arbitrary system. For illustration, this procedure is employed to derive robustness metrics for two example distributed systems. Such a metric can help researchers evaluate a given resource allocation for robustness against uncertainties in specified perturbation parameters.