Abstract: Based on the kinetic Shakhov model equation, a unifiedsimplified velocity distribution function equation describing gas transportphenomena for various flow regimes is proposed. The discrete velocityordinate technique is studied and applied to the velocity distributionfunction equation. With the decoupling technique of the DSMC methodand the unsteady time-splitting method, the gas-kinetic finite differencemethod for directly solving the velocity distribution functions isestablished by coupling and iteration. The discrete velocitynumerical integration methods are developed and applied to evaluate themacroscopic flow parameters at each point in the physical space. As aresult, a unified simplified gas-kinetic numerical algorithm is obtained for flows from rarefied transition to continuum. To test thepresent method, one-dimensional shock structure problems,two-dimensional flows past cylinder, and three-dimensional flows aroundsphere with various Knudsen numbers are simulated. The computational resultswith high resolution of the flow fields are found in good agreement with thetheoretical, DSMC, N-S and experimental data. The computing resultsconfirm a good precision and reliability of the algorithm in solving thegas dynamical problems from rarefied flow to continuum. The HPF parallelstrategy is studied for the gas-kinetic numerical method. The gas flowsaround three-dimensional sphere and spacecraft-like shape with variousKnudsen numbers are computed with massive scale parallel schemes. A good parallel efficiency and speed-up ratio have been found so that itis practical and possible that an HPF parallel algorithm can bedeveloped for solvingthree-dimensional complex problems in various flow regimes. The gas kinetic algorithm is extended and applied to study themicro -channel gas flows. The numerical algorithm is developed for thegas flows in two-dimensional short micro-channels with various Knudsennumbers. The classical Couette flows, the pressure-driven plane Poiseuilleflow, and the pressure-driven gas flows in two-dimensional shortmicro-channels are simulated and compared with the approximatesolutions of the linear Boltzmann equation, the related DSMC results, themodified N-S solutions with slip-flow boundary, and the experimentaldata. The numerical experience shows that the gas kinetic algorithm may be apowerful tool in the numerical simulation of micro-scale gas flows in theMicro-Electro-Mechanical System (MEMS).