Combining the SRIM'06 computer code and the formula for spectral-angular distribution of radiation from a particle moving in a medium in arbitrary trajectory, we studied numerically the structure of angular distributions of Cherenkov radiation from moderately relativistic heavy ions (RHI) taking into account the decrease of ions velocity due to stopping in radiator. The re-sults obtained clearly show that the width and the fine structure of the Cherenkov radiation in vicinity of Cherenkov cone depend strongly on several factors, e.g. mean and total energy losses, radiator thickness, square of the ion charge, emission wavelength and refractive index of the radiator material. This might be useful for experiments using RICH detectors of relativistic heavy ions.