Distributed Denial-of-Service (DDoS) attacks towards name servers of the Domain Name System (DNS) have threaten to disrupt this critical service. This paper studies the vulnerability of the cache server to the flooding DNS query traffic. As the resolution service provided by cache server, the incoming DNS requests, even the massive attacking traffic, are maintained in the waiting queue. The sojourn of requests lasts until the corresponding responses are returned from the authoritative server or time out. The victim cache server is thus overloaded by the pounding traffic and thereafter goes down. The impact of such attacks is analyzed via the model of queuing process in both cache server and authoritative server. Some specific limits hold for this practical dual queuing process, such as the limited sojourn time in the queue of cache server and the independence of the two queuing processes. The analytical results are presented to evaluate the impact of DDoS attacks on cache server. Finally, numerical results are provided for further analysis.