Shakedown theory for rate-independent materials has been successfully applied to discrete structures for many years, but has only recently been applied successfully to continua. A notable success is the use of the upper-bound theorem (Koiter’s theorem) to analyse different types of wear mechanisms of surfaces subjected to repeated sliding or rolling contacts. The present paper is concerned with the analogous geomechanics problem of analyzing wear mechanism of roads and pavements. In many of the less densely populated parts of the world pavements are of the “unbound type” where the top asphaltic layer is very thin, has no structural role in the response of the pavement, and serves only as a weatherproofing layer. In such pavements, the structure can be modelled as a rate-independent, pressure dependent, elastic-plastic material, using Mohr-Coulomb, critical state or other similar standard geomechanics model. The ongoing research described in this paper is concerned with computing the critical shakedown load associated with various failure mechanisms, such as subsurface and surface slip and rut formation. The optimal design, is obtained using various nonlinear optimization techniques including quasi-Newton and simulated annealing. Whilst the techniques involved have some resemblance to classical limit analysis methods, the optimal solutions are shown to be strikingly different.