Turbulent transonic freestream flow over a plane smooth surface embedded with smooth and rough circular arc bumps is computed and analyzed using the k turbulence model to determine the global effect of surface roughness on the shock/boundary layer interaction. Computations are done for various freestream Mach numbers, equivalent sand grain surface roughness heights of the bump, and radius of the bump. The influence of the increase in surface roughness height transcends over onto the shock boundary layer zone and the observations are discussed. It is observed that the surface roughness causes upstream movement of the shock, increases the skin friction coefficient, extends the separation length, reduces the pre-shock Mach number, and enhances the shock/boundary layer interaction zone.