We use dataflow graphs to represent the computational structure, analogous to Petri nets and Turing machines, and have developed a method for analyzing the reliability of computer systems modeled as dataflow graphs. Because of the hierarchical nature of dataflow graphs, systems can be analyzed at several levels of abstraction. Reliabilities of subgraphs can be calculated using either traditional techniques or dataflow approach presented here (recursively). The reliabilities of subgraphs can then be combined leading to decomposition-aggregation approach. The time needed for an actor to complete its operation is not included in our analysis of dataflow graphs. Incorporation of the time element compounds the problem and we have not studied it yet.