The properties of coherent X-radiation (CXR), generated in crystals by electrons in the tens of MeV energy range, were investigated theoretically. The analytical expressions for CXR spectral-angular and angular cross sections were obtained with the use of small-angle multiple scattering approximation. Our theoretical results are in good agreement with experiment. The obtained results can be used in designing quasi-monochromatic, tunable and polarized X-radiation sources based on the CXR process.