A viscoelastic model is proposed to describe the propagation of gravity waves into various types of ice cover. The ice-ocean system is modeled as a homogeneous viscoelastic fluid overlying an inviscid layer. Both layers have finite thickness. The viscosity is imagined to originate from the frazil ice or ice floes much smaller than the wavelength, and the elasticity from ice floes which are relatively large compared to the wavelength. A compact form of the dispersion relation is obtained. Under proper limiting conditions this dispersion relation can be reduced to several previously established models including the mass loading model, the viscous layer model and the thin elastic plate model. The full dispersion relation contains several propagating wave modes under the ice cover. The following two criteria are used to select the dominant wave mode: (1) wave number is the closest to the open water value and (2) attenuation rate is the least among all modes. The modes selected from those criteria coincide with the ones discussed in previous studies, which are shown to be limiting cases in small or large elasticity regimes of the present model. In the intermediate elasticity regime, however, it appears that there are three wave modes with similar wavelengths and attenuation rates. Implications of this intermediate elasticity range remain to be seen. The general viscoelastic model bridges the gap among existing models. It also provides a unified tool for wave-ice modelers to parameterize the polar regions populated with various types of ice cover.