Snow is a highly non-linear visco-elastic material characterised by a complex microstructure. In this paper we present a constitutive model for snow that is based on the axial and inelastic micro-structural deformations of the ice lattice. We determine the average micro-structural stress in the grain necks and then apply a strain-rate and temperature dependent viscosity law of pure ice to describe the deformation of the solid ice lattice. The law is valid for strain-rates E between 10^-7s^-1 and 10^-5s^-1. The constitutive model is validated using mechanical  tests performed with a specially designed deformation controlled triaxial apparatus. Stereological thin sections were taken of the experimental samples to determine the grain and bond size as well as co-ordination number. In a final step, we attempt to apply our micro-structural theory to determine a micro-structure based elasticity law, but without success. We conclude that the elastic and viscous behaviour of snow are governed by different micro-structural deformation processes.