Computational methods are widely used in prediction of complex flowfields associated with off-normal situations in aerospace engineering. Modern graphics processing units (GPU) provide architectures and new programming models that enable to harness their large processing power and to design computational fluid dynamics (CFD) simulations at both high performance and low cost. Possibilities of the use of GPUs for the simulation of external and internal flows on unstructured meshes are discussed. The finite volume method is applied to solve three-dimensional unsteady compressible Euler and Navier-Stokes equations on unstructured meshes with high resolution numerical schemes. CUDA technology is used for programming implementation of parallel computational algorithms. Solutions of some benchmark test cases on GPUs are reported, and the results computed are compared with experimental and computational data. Approaches to optimization of the CFD code related to the use of different types of memory are considered. Speedup of solution on GPUs with respect to the solution on central processor unit (CPU) is compared. Performance measurements show that numerical schemes developed achieve 20 to 50 speedup on GPU hardware compared to CPU reference implementation. The results obtained provide promising perspective for designing a GPU-based software framework for applications in CFD.