A parallel implementation of a previously developed finite volume algorithm for the solution of two-dimensional, unsteady, compressible Euler equations is given. The conservative form of the Euler equations is discretized with a second order accurate, one-step Lax-Wendroff scheme. Local time stepping is utilized in order to accelerate the convergence. For the parallel implementation of the method, the solution domain is partitioned into a number of subdomains to be distributed to separate processors for parallel computations. The exchange of information between subdomains is due to overlapped boundaries at the block interfaces. The sequential solver is parallelized using the PVM (Parallel Virtual Machine) message-passing library routines in a master-slave paradigm. A PC cluster of Pentium processors running on Linux operating system, which are connected over a local network using Transmission Control Protocol/Internet Protocol (TCP/IP), is used for computations. PVM version 3.4 is used as the communication library. To test the performance of the parallel algorithm, subsonic, transonic and supersonic channel flows over a Ni-bump are considered.