The deployment of multiple small cells with low-power and low-cost Base Stations (BSs) offers new opportunities for increased traffic demands in Ultra Dense Networks (UDN). However, an instant increase in traffic flows, and subsequent problems with communications caused by the huge demand of users, cannot be met by the existing infrastructure since the users consume all of the network resources in unexpected turn of events (e. g. in the aftermath of large disasters). Hence, this paper aims to design a resilient UDN in order to provide an acceptable Quality of Service (QoS) in the face of unusual traffic challenge. First, by considering this extreme communication environment, we propose a queuing-based approach to model BSs and then define a resilience parameter to guarantee desired QoS. Second, we investigate the deployment of Unmanned Aerial Vehicles (UAVs) to serve as flying BSs. Here, we determine the required number of UAVs and optimal locations for delivering coverage. Our numerical results show that the proposed model has increased the resiliency by 27%, thus constituting a more resilient UDN.