Abstract: A domain decomposition method of Euler equations is applied to a two dimensional transonic and supersonic flow. The flow region is divided into distinct regions, a zonal interface conservative technique is presented on basis of flux-vector splitting methods and characteristics theory of information propagation then interfacing these regions separately. Two dimensional transonic and supersonic flow field including arc bump and airfoils are calculated. Results of domain decomposition method are coincident very well with that of continuous single region solution. Parallel computing method using PVM parallel environment is proposed. “First-in First-out” synchronization strategy is applied in parallel programming model. An efficient method of high parallel speedup ratio is applied and influencing factors of parallel computing are disucssed.