Macaroni channel structure is used popularly in 3-D NAND flash memory where the memory cells are connected in series. A model of inner potential in the subthreshold regime for the whole string of three transistors is presented and verified with the TCAD simulations. By using this model, the operation of the string and the interaction between transistors are investigated. Relative position dependence between transistors is also investigated. The obtained model can be used to predict the interference effect and be helpful in the design of the 3-D NAND flash memory cell.