In this work, a new method for the atomistic simulation of ion-channeling spectra for ion irradiated Si is reported. The disordered crystal is represented by a supercell populated with point defects and then relaxed through a static energy minimization procedure based on empirical potentials. By including this supercell in a computer code for the simulation of ion-channeling spectra, we try to reproduce multi-axial results in the slightly damaged surface region of high-energy ion implanted Si. In spite of the simple assumptions on the nature of defects, we find that our method substantially improves the multi-axial data fit in comparison with that obtained under the usual assumption of random point defects.