The use of QoS parameters to evaluate the quality of service in a mesh network is essential mainly when providing multimedia services. This paper proposes an algorithm for planning wireless mesh networks in order to satisfy some QoS parameters, given a set of test points (TPs) and potential access points (APs). Examples of QoS parameters include: probability of packet loss and mean delay in responding to a request. The proposed algorithm uses a Mathematical Programming model to determine an adequate topology for the network and Monte Carlo simulation to verify whether the QoS parameters are being satisfied. The results obtained show that the proposed algorithm is able to find satisfactory solutions.