System decomposition is a novel technique for modeling the dependability of complex systems without constructing a single-level Markov Chain (MC). This is demonstrated in this paper for the availability computation of a class of multiprocessors that uses 4*4 switching elements for the multistage interconnection network (MIN). The availability model is known as task-based availability, where a system is considered operational as long as the task requirements are satisfied. The authors develop two simple MC's for the processors and memories and solve them using a software package, called HARP. The probabilities of i processing elements (PE's) and j memory modules (MM's) working at any time t, denoted as Pi(t) and Pj(t), are obtained from their corresponding MC's. The effect of the MIN is captured in the model by finding the number of switches required for the connection of i PE's and j MM's. A third MC is then developed for the switches to find the probability that the MIN provides the required (i*j) connection. Multiplying this term with Pi(t) and Pj(t), the probability of an (i*j) working group is obtained. The methodology is generalized to model arbitrary as well as larger size systems. Transient and steady state availabilities are computed for a variety of MIN configurations and the results are validated through simulation.>