The TOFD (Time of Flight Diffraction) technique is a classical ultrasonic inspection method used in ultrasonic non-destructive evaluation (NDE). This inspection technique is based on an arrangement of two probes of opposite beam directions and allows a precise positioning and a quantitative evaluation of the size of cracks contained in the inspected material thanks to their edges diffraction echoes. Among the typical phenomena arising for such an arrangement, head waves, which propagate along the specimen surface and are chronologically the first waves reaching the receiver, are notably observed. Head wave propagation on planar surfaces in TOFD configurations is well known. However, realistic inspection configurations often involve components with irregular surfaces, like steel excavated specimens. Surface irregularity is responsible for numerous effects on the scattering of bulk waves, causing the melting of surface and bulk mechanisms in the head wave propagation. In order to extend the classical ray approach on these complex cases, a generic algorithm of ray tracing between interface points (GIRT) has been designed. With respect to time of flight minimization (i.e. the Generalized Fermat's Principle), ray paths can be computed by GIRT for different natures of waves scattered by the complex surfaces or by flaws. The head wave fronts computed by GIRT are notably in good agreement with FEM simulated results. This algorithm, based on pure kinematic analysis of waves propagation, represents a first step in the future development of a complete ray theory for head waves simulation on irregular interfaces.