Noise attenuation by sonic crystal noise barriers occurs mainly in specific frequency bands (bandgaps), due to a mechanism called Bragg scattering, which is the result of destructive interference between multiple reflections. To improve their performance, sound-absorbing materials may be used to coat the rigid scatterers, increasing attenuation in other frequency bands. In this work, the Method of Fundamental Solutions (MFS) is used to evaluate the performance of sonic crystal noise barriers with cylinders covered by porous and granular materials simulating the volume of the absorbent material using equivalent fluid models for porous or granular materials. The proposed numerical models were validated by experimental tests and, afterwards, these numerical models were verified through the comparison with results obtained using the Finite Element Method (FEM). Finally, several numerical tests were performed in order to understand/predict the acoustic behavior of the sonic crystal noise barriers covered with porous concrete.