In this paper, a methodology for depositing wear- and corrosion-resistant layers of geometrically more complex tracks on metal substrates is presented. The corresponding mathematical model includes the temperature field produced by the laser beam, the field of residual mechanical stresses, and the efficiency of utilization of the delivered powder material. The computations are realized using the finite element method, with a substantial improvement in processing the time-variable geometry of the investigated system being found, based on the introduction of two specific matrices that characterize both the surface on which the tracks are cladded as well as the track itself. The proposed technique is illustrated by cladding an angled helix on a metal surface. Selected results are successfully verified by experiments.