<b>Purpose</b> <p>Simulating tissue deformation and flow alterations induced by external compression typically requires fluid–structure interaction (FSI) analysis, which is computationally demanding. This study presents a multi-fidelity FSI framework that efficiently captures tissue mechanics and hemodynamic responses to dynamic external pressure and demonstrates its applicability to compression therapy.</p> <b>Methods</b> <p>We developed an FSI model that couples a one-dimensional deformable blood flow formulation with the three-dimensional (3D) Cauchy equation of motion. Model performance was evaluated by comparing the multi-fidelity and full FSI solutions in simplified cylindrical and subject-specific geometries. As a practical demonstration, the framework was applied to simulate a full-cycle pulsatile intermittent pneumatic compression (IPC) operation.</p> <b>Results</b> <p>The model efficiently reproduced tissue deformation and hemodynamic changes under external compression, yielding &lt;1% flow-rate error in both geometries and &lt;2% pressure error in the simplified geometry for most of the cycle, with good agreement in the subject-specific geometry. Computational cost was reduced by a factor of 9 in the cylindrical geometry and 46 in the subject-specific geometry relative to full 3D FSI. In the IPC application, the model captured dynamic behavior over an extended temporal scale, completing a full cycle in 457&#xa0;s for the simplified geometry and 42.2&#xa0;min for the subject-specific geometry.</p> <b>Conclusion</b> <p>This multi-fidelity FSI framework enables efficient and accurate simulation of tissue deformation and hemodynamic responses under external pressure, providing a tractable platform for large-scale parametric and optimization studies. Its application to IPC highlights potential to enhance therapeutic device design and support broader applications in biomedical modeling and medical device development.</p>