The paper is devoted to modeling and optimization of reliable wireless mesh networks that employ directional antennas. We introduce two mixed-integer programming formulations that allow to simultaneously characterize routing patterns and transmission schedules. The first model allows for maximizing the minimal flow in a network. The second model involves reliability constraints and aims at minimizing the number of used directional antennas. In both cases locations of mesh routers are known. However, the number of installed radio interfaces and their directions are subject to optimization. We discuss a way of solving a cost minimization problem based on the introduced characterization, and present an extensive numerical study that illustrates the efficiency of the solution algorithm. We also provide an algorithm capable of verifying feasibility of obtained solutions. Moreover, in rare cases of failed verification, the algorithm provides additional constraints that should be added to the problem.