A semiquantitative, phenomenological model for low energy ion interactions with surfaces is developed. The model represents a generalization of the qualitative subplantation model of Lifshitz et al., Phys. Rev. B 41, 10 468 (1989). A general equation for describing ion solid interactions, including film growth processes, is introduced. This model, for the first time, describes the three major contributions to such interactions, i.e., ion penetration, defect production, and radiation enhanced diffusion, in terms of simple analytical equations. In this first article, the basic assumptions of the model are described and the concepts are demonstrated for the example of rare gas ion interaction with graphite. The model is developed in both a simple static form and a more complex dynamic one, the latter is applicable to ion fluence-dependent phenomena. The model provides calculated values of experimentally observable quantities such as the primary ion concentrations retained in the surface and subsurface layers. It also provides estimates of quantities that are difficult to measure such as penetration thresholds, displacement thresholds, and diffusion rates.