Abstract: Gas Kinetic Unified Algorithm (GKUA) based on Boltzmann model equations is proposed for simulating aerodynamics problems covering various flow regimes. In this algorithm, molecular motions are decoupled from collisions by traditional Computational Fluid Dynamics methods, so that the calculation e ciency would be quite low at the limitation of stabilization conditions of explicit schemes when simulating supersonic flows especially which are near-continuum and continuum flows. In order to improve the e ciency and expand engineering practicability, an implicit method for Boltzmann model equations is constructed by using LU-SGS (Lower-Upper Symmetric Gauss-Seidel) method and cellcentered finite volume method, and multi-block patched grid technique is used in physical space. The present computed results of two side-by-side cylinders in transitional flow regime are found in good agreement with those from Direct simulation Monte-Carlo method simulation. The dependability and feasibility for simulating problems covering various flow regimes by the present method are validated.