This paper deals with the development of a semi‐analytical model for the fast computation of the quasi‐static field induced by any eddy current probe in a 3D conductor of complex shape. The workpiece is considered as a planar half‐space mock‐up with an interface air conductor characterized by an arbitrary 2D surface a(x, y). The curvilinear coordinate method consists in introducing a change of coordinates to be able to write analytically and easily the boundary conditions at the interface air‐metal. Due to the novel generalized metric space, the covariant form of Maxwell equations must be considered. The curvilinear coordinate method is widely used in the optical community for the analysis the diffraction phenomenon on gratings. The method has been applied recently for eddy current calculations in the planar case for 2.5D configurations characterized by a 3D eddy current probe and a 2D layered stratified conducting media. By an extension to 3D problems, this work constitutes the preliminary task for the development of a complete numerical model, which has the capability to address very complex eddy current nondestructive testing configurations such as a stratified layered media constituted by a set rough interfaces. For that purpose, the modal formalism is described for the first time in the 3D case, and several numerical experiments show the validity and the efficiency of the fast numerical model in comparison to the finite element method.