The mathematical principles and derivation of a linear visco-elastic multilayer computer program are described. The mathematical derivation is based on Fourier Transformation. The program is called VEROAD, which is an acronym for Visco-Elastic ROad Analysis Delft. The program allows calculation of physical quantities like time-dependent displacements, stresses and strains, permanent deformations and dissipated energies in a multi-layer system built of visco-elastic materials. All the quantities thus depend on the velocity of the traffic, which explicitly comes into the calculations. The material model assumes the bulk modulus to be elastic and the shear modulus to be visco-elastic. The latter follows the Burgers'model. For illustrative purposes, some mechanical analyses of asphaltic road structures are shown.