The problem of stress singularity in a substrate-coating system is dealt with the use of elasticity theory approach, where a biharmonic equation in the polar coordinates is employed to solve for coating free edge of various configurations. This allows for the generation of a singularity pattern in the studied configurations. The dependences of the singularity on the ratio of the elastic characteristics of the substrate-coating system and on the configuration of the coating free edge are obtained. The order of the stress singularity is found for high velocity oxy-fuel (HVOF) thermally sprayed nanostructured WC-17Co coatings. In particular cases, the problem has shown to degenerate into fracture mechanics problem involving a crack in a homogeneous material or into an elasticity theory problem associated with homogeneous wedges and notches.