This work utilizes an immersed-boundary method to simulate the effects of an array of aeroelastic mesoflaps in controlling oblique shock/turbulent boundary-layer interactions. A loosely coupled approach is adopted for the fluid-structure interaction problem, with separate solvers used for the fluid and structural domains. The mesoflaps are rendered as immersed objects for the fluid solver and modeled as cantilevered Euler-Bernoulli beams for the structural solver. Determination of the aerodynamic loads acting on the mesoflap surfaces from the surrounding fluid is done using a nearest neighbor approach combined with a bi-linear interpolation scheme. Simulations are performed for a Mach 2.46 shock / boundary layer interaction with and without control, based on experiments conducted at University of Illinois at Urbana-Champaign. Both Reynolds-averaged Navier-Stokes (RANS) and hybrid large-eddy/Reynolds-averaged Navier-Stokes (LES/RANS) turbulence closures are used. For the computations of the flow with mesoflap control, both 2-D quasi-steady and 3-D dynamic simulations of the fluid-structure interaction problem are performed. Comparisons made with experimental laser Doppler anemometry data and wall pressure measurements for flows with and without control show reasonable agreement, with better predictions away from the separation region. An analysis of the flow indicates that the mesoflap control system does not eliminate axial flow separation. Also, analysis of the frequency content of the mesoflap deflections suggests that a correlation might exist between the dominant frequency of the flap deflection and the low-frequency shock motion observed in separated flows.