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Data structure plays an important role in conventional computer. The motivation of this paper is to study the linear data structure in DNA computer, which can help to improve the application capability of DNA computer. We take stack and queue as an example to discuss their design and implementation. Firstly, their storage structures are discussed. Then, we propose the nucleotide-encoding for all components of stack and queue in DNA computer. And, all bio-operations over stack and queue are described. All the biological technology mentioned in this paper can be practically implemented in the laboratory. Based on this work, other data structures could be further studied and developed.