Summary: We report on thermal noise from the internal friction of dielectric coatings made from alternating layers of \(\text{Ta}_2\text{O}_5\) and \(\text{SiO}_2\) deposited on fused silica substrates. We present calculations of the thermal noise in gravitational wave interferometers due to optical coatings, when the material properties of the coating are different from those of the substrate and the mechanical loss angle in the coating is anisotropic.