This SBIR Phase I project proposes to develop a unified gas-kinetic computational algorithm, which can cover the whole flight regime, including continuum, transitional, and rarefied. The method is not only able to extend current computational aerodynamic and aerothermodynamic methods to a much wider class of problems such as hypersonic rarefied flows but also able to significantly improve the accuracy of current computational aerodynamic and aerothermodynamic methods in the continuum regime. Implementation of this algorithm into the current Euler/Navier-Stokes codes is relatively straightforward. The method can be implemented for both structured and unstructured grids.