Tensegrity　robotic　fish　is　an　emerging　solution　in　the　field　of　robotic　fish,　and　its　dynamic　model　plays　a　crucial　role　in　guiding　the　improvement　of　swimming　performance.　However,　there　is　a　lack　of　in-depth　research　in　this　area.　This　paper　proposes　a　planar　dynamic　model　for　the　tensegrity　robotic　fish,　which　can　be　used　to　simulate　and　investigate　the　influence　of　body　stiffness　on　swimming　performance.　An　equivalent　modeling　approach　is　introduced　for　the　soft　fish　skin　and　tail　fin　to　consider　their　effects　of　flexibility　on　the　robotic　fish’s　swimming　motion.　A　hydrodynamic　discretization　model　based　on　virtual　nodes　is　proposed　to　incorporate　hydrodynamic　effects　such　as　drag　force,　lift　force,　and　added　mass　into　the　fish’s　vertebral　column.　By　integrating　the　above　models,　the　dynamic　model　for　the　tensegrity　robotic　fish　is　established　after　embedding　the　tail　joint　constraints.　The　method　of　reconstructing　fish　body　waves　in　the　simulation　is　provided　to　calculate　fish　swimming　characteristics.　The　parameter　identification　method　for　the　drag　coefficient　and　torque　coefficient　is　proposed.　The　dynamic　model　of　the　tensegrity　robotic　fish　is　verified　using　swimming　experimental　data.　By　conducting　numerous　numerical　simulations,　the　effects　of　the　body　stiffness　distribution,　tail　fin　stiffness,　and　fish　skin　stiffness　on　the　swimming　performance　are　analyzed.　The　simulation　results　reveal　the　significant　role　of　adjusting　body　stiffness　in　enhancing　the　swimming　characteristics　of　the　robotic　fish.　©　The　Author(s),　under　exclusive　licence　to　Springer　Nature　B.V.　2024.