Effect of elastic anisotropy on indentation-induced thin film interfacial delamination, especially, at the initiation and early growth stage, is examined. The indentation load is modeled as a constant pressure over an expanding semi-spherical cavity. The delamination process is approached by a cohesive zone model. The rest of the problem is formulated within the general anisotropic elasticity theory, and solved numerically by the boundary element method employing a special Green's function for multilayers. The material system of a Cu(0 0 1) film on a Si(0 0 1) substrate is studied as an example. The interfacial damage initiation and crack development under indentation are captured in the simulation. By comparing the predictions with the materials being modeled as isotropic and as anisotropic (of the cubic symmetry as they are), it is shown that the elastic anisotropy of the copper film plays a significant role in determining the delamination pattern. In the isotropic model, the delamination crack fronts are circular reflecting the problem axisymmetry. In contrast, crack fronts are square with rounded corners in the anisotropic case. This significant difference necessitates a three-dimensional anisotropic stress analysis of the indentation-induced delamination of strongly anisotropic films.