In constructing the road, asphalt pavement is most useful one. And then, when we consider of the structure of road, all pavement slabs are vescoelastic bodies, but in the past, almost investigators analyzed the stress distribution of pavement slabs by treating them as elastic bodies. So, the author studied behaviors of viscoelastic bodies and at first considered asphalt mixtures to be visco elastic bodies. The combination of a spring and a dashpot connected in series is known as Maxwell element. In generalized Maxwell element, it is reported by Mr, Kenji Ishihara that the definition of (transient creep function with discrete spectrum) may be given to the ratio σ/ε in [numerical formula] (1) where ε=ε_0t The compressive tests subjected to a linearly increasing strain ε_0t were tried and their stress-strain curves were drawn at different rates of strains. And we could decide the visco-elastic constants of asphalt mixtures by their stress-strain curves. The results of experiments and the method of deciding the viscoelastic constants are mentioned in this paper.