Computations were performed to investigate the flowfields of normal shock-wave/boundary-layer interactions with mesoflap control. The control system involves placing a mesoflap array beneath the interaction, allowing high-pressure air from the flow downstream of the shock wave to recirculate through a cavity into the low-pressure flow upstream of the wave. The case of a normal shock at a Mach number of 1.4 interacting with the turbulent boundary layer on a flat wall was first considered, and the predictions were compared with experimental results. A number of fixeddeflection mesoflap simulations have been performed to understand the correlations between flap deflections, downstream boundary layer characteristics and stagnation pressure recovery. The prescribed steady-state deflections were based on qualitative aeroelastic experimental observations. It was found that the magnitude of the deflection of the upstream mesoflaps is key to providing a significantly increased "lambda-foot" benefit, which is critical for improved stagnation pressure recovery. The number of flaps and their locations were also found to significantly affect the stagnation pressure recovery and downstream boundary layer characteristics. In addition, it was found that cavity depth does not play a significant role in pre-compression or smearing of the normal shock (i.e., stagnation pressure recovery).