Very recently, ESEAP mutual authentication protocol was designed to avoid the drawbacks of Wang et al. protocol and highlights that the protocol is protecting all kind of security threats using informal analysis. This work investigates the ESEAP protocol in security point of view and notices that the scheme is not fully protected against stolen verifier attack and does not provide user anonymity. Furthermore, the same protocol has user identity issues, i.e., the server cannot figure out the user identity during the authentication phase. Later we discuss the inconsistencies in the security analysis of ESEAP presented by RESEAP.