Recently standardized, WiMAX promises high data rates over long ranges. It defines two modes of operation Point-to-Multi-Point PMP and MESH. In the PMP mode, subscriber stations (SSs) connect to the base station (BS) in single-hop transmissions. The mesh mode on the other hand, allows direct communications between SSs. WiMAX mesh networks constitute a real solution for extending the coverage of the BS. They can be used for providing access into under-covered zones like rural areas and hard-to-wire areas. Several aspects affect the performance of the mesh, such as routing, scheduling and SS locations which when optimized, result in improved performance in term of capacity. In order to cover a specific area, we propose a placement algorithm that adequately places the SSs using routing and scheduling algorithms that we have previously proposed for the purpose of maximizing the capacity. Knowing that placement problems are NP-Hard, we design a heuristic with two variants and we show by simulations, that our algorithms, compared to the intuitive bottom-up approach, always find the smallest number of SSs, but also guarantee a required data rate.