We present a session initiation protocol (SIP) network design for a voice-over-IP network to prevent congestion caused by people calling friends and family after a disaster. The design increases the capacity of SIP servers in a network by using all of the SIP servers equally. It takes advantage of the fact that equipment for voice data packets is different from equipment for signaling packets in SIP networks. Furthermore, the design achieves simple routing on the basis of telephone numbers. We evaluated the performance of our design in preventing congestion through simulation. We showed that the proposed design has roughly 20 times more capacity, which is 57 times the normal load, than the conventional design if a disaster were to occur in Niigata Prefecture struck by the Chuetsu earthquake in 2004.