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A computational method for solving the 3D Euler equations is studied. The method is based upon an upwind flux-difference splitting scheme by Osher, exhibiting an implicit mechanism for numerical viscosity, in connection with an explicit time-marching finite-volume technique. The computer program is developed to run efficiently on both a scalar computer and the Cyber 205 vector computer. Demands made by the necessity of vectorizability of the code, on algorithm, data-structuring, and the code itself, are discussed. Also, the large data sets involved in 3D calculations, appear to impose severe claims on central-memory size, I/O devices and line connections. The method is tested for a transonic and supersonic quasi-two-dimensional channel flow. The Euler model is found to give an accurate simulation of aerodynamic phenomena in the channel.