A new approach to modelling probabilistic and stochastic engineering systems using graph theory is outlined. This approach emphasizes the introduction of probabilistic and stochastic concepts at the very beginning of the model building process. This is in marked contrast to past tendencies to add probabilistic concepts to the end of an otherwise deterministic model building process. The development of topological models founded on oriented probabilistic measurements is given. which leads to the identification of some useful statistical properties of the’ random interconnection equations’. The development of probabilistic component models is given, where a component can be characterized independently of other components. Methods for automatically building the second moment representation of the Mixed Nodal Tableau are discussed. The application of the above theory to the probabilistic analysis of a pipe network problem is briefly described.