The hydrodynamic interaction force between autonomous underwater vehicles (AUVs) operating in tandem can adversely affect the hydrodynamic prediction of individual AUVs and the formation control of the tandem fleet. Accurate modeling of hydrodynamic interaction forces is crucial to the model-based controller design of AUVs. In this paper, we innovatively propose a modeling method that can describe the hydrodynamic interaction relationship accurately and continuously (when the spacing between adjacent AUVs changes). First, an accurate hydrodynamic model for individual AUVs in tandem fleets is established by modifying the typical model through the consideration of memory effects. Second, a model of hydrodynamic interaction forces is derived by subtracting hydrodynamic forces acting on a single AUV operating independently from those acting on an AUV operating in tandem. To enable this model to continuously describe the hydrodynamic interaction relationship when the spacing changes, this model is further derived by taking the spacing as an independent variable based on the parameter conversion method. Finally, planar motion mechanism (PMM) tests are carried out using the computational fluid dynamics (CFD) method to verify the accuracy and continuity of the proposed modeling method. The results show that compared with the typical model, the average error of hydrodynamic forces predicted by the proposed model is reduced by 5.36%, which verifies the feasibility and effectiveness of the proposed modeling method.