This paper deals with the numerical study of frictionless viscoelastic tyre/road contact. The present macro-scale approach takes into account both the viscoelastic behaviour of the tyre and the roughness of the road surface by solving the contact problem between a rough multi-indentation surface and a viscoelastic half-space. The method relies on the fact that a viscoelastic solution can be instantaneously reduced to an elastic solution. A simplified description of viscoelastic material behaviour by a rheological model is used. In order to evaluate the efficiency of the method, numerical contact forces for a simple surface composed of seven rigid spherical tips are compared to the results of a classical matrix inversion method. The correlation between both methods is good. The same comparison for a small sample of road surface was performed and the global differences on the contact forces are below 5%. It is observed that the multi-asperity method can predict tyre/road contact with a rather good accuracy and with a drastically reduced calculation time in comparison with classical methods. Then numerical evaluation of tyre/road viscoelastic contact forces for different road textures is compared to elastic prints in order to assess the effect of the viscoelasticity. The authors believe that the present approach is useful for applications such as rolling noise and rolling resistance prediction.