This paper consists of two parts: the first provides the theoretical foundations for analyzing parallel programs and illustrates how the theory can be applied to estimate the execution time of a class of parallel programs being executed on a MIMD computer. The second part describes a program analysis system, based on the theoretical model, which allows a user to interactively analyze the results of executing (or simulating the execution) of such parallel programs. Several examples illustrating the use of the tool are presented. A novel contribution is the separation (both at the conceptual and the implementation levels) of the machine-independent and the machine-dependent parts of the analysis. This separation enables the users of the system to establish speed-up curves for machines having varying characteristics.