||The Bhatnagar-Gross-Krook (BGK) collision model is an approximation to the Boltzmann’s equation. Based on this model with the Navier-Stokes (NS) equations, the gas-kinetic BGK-NS scheme was developed for computing continuum flow. Furthermore, with the discretization of particle velocity space, a unified gas-kinetic scheme was constructed as an extension of the BGK-NS scheme, being used for regimes with different scales of Knudsen number. In this thesis, the unified gas-kinetic scheme is used to compute low-Mach-number shocks. The shock structures are analyzed through shape factor, maximum-slope shock thickness and density-temperature separation. These results are compared to the result using direct simulation Monte Carlo (DSMC) methods for both hard-sphere and Maxwell gases, and also experimental results by using argon. Comparisons are also made corresponding to Burnett and Navier-Stokes solutions.