Survivability is a crucial property for computer systems that support critical infrastructures of our society. A variety of survivability definitions and evaluation methods for traditional software have been proposed. However, for those in paradigm of Service Oriented Architecture (SOA) where the computing settings are intrinsically open, these methods are no longer applicable. In this paper we study survivability aspects in SOA systems. A formal survivability definition is proposed according to new characteristics of SOA. We also set up an extended framework in which survivability can be evaluated and advertised as a special multidimensional Quality of Service (QoS) property. In particular, we introduce a novel Hidden Markov Model (HMM) based method for survivability evaluation.