A model for the dependence of the electrical conductance, G, with the strain induced by external mechanical stress in conducting particles-polymer composites is presented. The model assumes that the percolation probability between neighboring particles must depart from a scale-invariant behavior but saturate at moderated-high strains, reaching percolation path’s saturation, with sigmoid dependence. This dependence is obtained by proposing a dynamic picture where contacts or bonds between neighboring particles are created but also destructed when a stress is applied and relatively moderated or high strains, ε, are produced in the composite. The electrical conductance of prepared graphite-polydimethylsiloxane composites were measured as function of the applied pressure and fitted by the presented model. The elastic response to the uniaxial compression was studied using a texture analyzer. The possibility of nonuniversal effects in the conduction critical exponent, t, was taken into account. It is concluded that the saturation of the response in the G versus ε plots cannot be assigned to nonuniversal behavior of the exponent t, or to saturation of the elastic response. On the other hand, the presented model accounts for all the main experimental features observed in these systems and for previously reported data of elastomer composites. The simulated behavior of the piezoresistivity coefficient is also in qualitative agreement with previous reports.