This paper is concerned with detection and prevention of weaknesses in the design of security protocols. These weaknesses can be exploited by an attacker mounting attacks that compromise the security of the protocol. A novel theory defining weaknesses caused by the symmetry of cryptographic messages in protocols is introduced. This theory incorporates new rules describing the cases when the symmetry of messages has a structural weakness that is exploitable by parallel session attacks. Further, the rationale behind the Symmetry rules is presented and the structures of detected generic attacks for each rule are provided. Additionally, the Symmetry rules are applied to a protocol that is vulnerable to a parallel session attack. It is demonstrated that the proposed theory successfully detects the weaknesses caused by the symmetry of protocol messages, which lead to parallel session attacks.