Wear is the process of material removal under abrasion. Multi-material systems are characterized by non-uniform wear-rates that are leading to non-planar profiles under polishing. Some recent iterative models have predicted with success the well established experimental fact, that under an initially uniform pressure load, multi-component wearing surfaces reach asymptotically a steady-state profile that continues to recess at a constant rate. In a first part, a continuous model is derived from the original iterative scheme, and extrapolated to a mathematical, abstract, but versatile framework. It is shown that the steady-state can be computed directly by solving a time-independent elliptic partial differential equation, providing a substantial computational gain against the first iterative scheme. In a second part, this formulation is used to apply modern shape optimization methods to optimize wear performance of bi-material systems. Several objectives for systems undergoing wear are identified and formalized with shape derivatives. As an example, the unit-cell of 2D multi-material composites is optimized using a level-set based method. A minimum feature size must be taken into account to avoid the convergence of minimizing design sequences toward composite materials. To address this issue, a variant of a the level-set topology optimization method is developed . Through the use of a single updating equation, this scheme conveniently enforces volume equality constraints, controls the complexity of design features with a perimeter penalization, and nucleates material inclusions with the use of the topological gradient. Keywords: topology and shape optimization, wear, multi-composite surface, level-set methods.