No actual explanation for the relatively low limit of the giant magnetoimpedance effect (GMI), in magnetostrictive materials, is now available. Neither the damping of the domain walls nor the dynamics of the magnetization rotation lead to values in agreement with the experience. In this paper we study the magnetoelastic influence on GMI. Magnetoelastic effects are responsible of permeability resonance and relaxation at low frequencies, but they have not been taken into account up to now. A limiting effect on magnetoimpedance, directly related to the sample saturation magnetostriction, is expected on the basis of our analysis. This result explains the well-known phenomenology of the GMI in magnetostrictive materials that, regardless the anisotropy strength, strongly depends on the value of the saturation magnetostriction. Recent experimental data confirm the predictions of the model.