The anti-plane displacement discontinuity method is applied to establish the Fredholm integral equation of the first kind for the orthotropic Functionally Graded Material (FGM) coatings subjected to static/dynamic shears. The shear modulus and mass density are assumed to vary exponentially through the thickness. The static and dynamic fundamental solutions with anti-plane displacement discontinuity are derived for orthotropic FGM coating by using Fourier transform method and Laplace transform method. It has been shown that the transformed fundamental solution with orthotropic coatings has the same order of hyper-singularity as in the static case, i.e. O(1/r2), and the Chebyshev polynomials of the second kind are used to solve the integral equations numerically. The time dependent stress intensity factors are obtained directly from the coefficients of the Chebyshev polynomials with the aid of Durbin’s Laplace transform inversion method. A comparative study of FGM versus homogeneous coating is conducted, and the dependence of the stress intensity factors in the coating/substrate system on the material property (orthotropic) and thickness of coating is examined. Two examples including the static/dynamic loads are given as benchmarks for the numerical methods and application in composite engineering.