Kinematic and dynamic performance of a parallel mechanism is, to some extent, determined by its topological structure, so topological structure analysis and synthesis is very important to research and application of parallel mechanisms, especially the parallel robot mechanisms. In order to achieve computer aided topological structure analysis and synthesis of parallel mechanisms, the topological structure of parallel mechanism must first be represented symbolically. An algebraic symbolic description system was proposed for parallel mechanisms on the basis of SOCbased mechanism composition principle. With this symbolic description system, topological structure of any parallel mechanism can be expressed as a symbolic polynomial, each item of the polynomial represents a branch of the parallel mechanism. The transitivity of kinematic pair orientation relations was discussed and symbolic representations of different kinematic pair relations were introduced. Based on this symbolic description system, position and orientation characteristic (POC) set of parallel mechanisms can be derived easily with the help of a computer program, i.e. POC set of a branch was sum of the POC set of each kinematic pair in this branch and POC set of the complete parallel mechanism was product of the POC set of each branch. The proposed symbolic description system features the algebraic property of a symbolic computer language, so it can be used reliably in computer aided mechanism studies. Work in this paper provided a theoretic basis and an effective method for computer aided analysis and automatic generation of parallel mechanisms.