Pavement and railtrack design is of huge importance to society and yet the theoretical basis for most current design methods is still very simplistic and crude (Brown, 1996; Yu, 2006). This paper is part of a concerted effort at the Nottingham Centre for Geomechanics to develop improved theoretical foundations for pavement and railtrack design. It is mainly concerned with the development of rigorous lower-bound solutions for shakedown of cohesive-frictional materials under three-dimensional moving traffic loads. Compared with previous studies, two important aspects are taken into account. First, this paper considers a more general case of elliptical contact area between traffic and material surface, as most previous lower-bound studies considered the traffic load is applied through an infinite long roller. Secondly, by introducing a critical self-equilibrated residual stress field, this shakedown problem is reduced to a formulation in terms of a load parameter only. By using a simple optimisation procedure, the maximum load parameter leads to a lower-bound shakedown limit to this problem. Results for the special case of circular contact area are also presented in analytical form, which can then be readily applied for practical design.