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DNA is used as self-nanomaterials to assemble into specific structures. DNA tile provides a new idea for the application of DNA tile in the field of computing. Recent years, Queue and Stack are important linear data structures which are used in various software systems widely. The implementation of DNA based queue and stack has been studied continuously for many years. In the traditional DNA computing, queue and stack are mostly realized by DNA strands displacement, restriction endonuclease and ligase were used. However, as an active material, it has a high requirement for enzyme experimental conditions. The purpose of this paper is to implement queue and stack structures using non-enzyme systems. The rule of Queue is characterized by FIFO (first in first out), which allows for insertion at one end of the list and deletion at the other. The rule of Stack is characterized by FILO(first in last out), which allows for insertion and deletion at one end of the list. We are aimed to implement Queue and Stack using self-assembly and disassembly via DNA Tiles. No enzymes are needed for the whole experiment. As an enzyme-free system, it provides a new method to implement stack and queue.