This paper deals with problems of computer networks survivability. We present and discuss survivability aspects of Content Delivery Networks (CDNs) and other services based on the anycast paradigm. After that, we propose a new unified approach to network survivability. This approach assumes using jointly survivability mechanisms for both kinds of traffic: anycast (oneto-one-of-many access to content servers) and unicast (one-to-one exchanging of data between individual users). We formulate a new optimization model for this scenario that can be used for development of algorithms. The optimization problem is NP-complete. The objective function is function of lost flow due to a failure of any single link. To our knowledge this problem have not received much attention in the literature. We provide also a numerical example to illustrate the proposed approach.