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Abstract Cardiomyocytes are viscoelastic and key determinants of right ventricle (RV) mechanics. Intracellularly, microtubules are found to impact the viscoelasticity of isolated cardiomyocytes or trabeculae; whether they contribute to the tissue-level viscoelasticity is unknown. Our goal was to reveal the role of the microtubule network in the passive anisotropic viscoelasticity of the healthy RV. Equibiaxial stress relaxation tests were conducted in healthy RV free wall (RVFW) under early (6%) and end (15%) diastolic strain levels, and at sub- and physiological stretch rates. The viscoelasticity was assessed at baseline and after the removal of microtubule network. Furthermore, a quasi-linear viscoelastic (QLV) model was applied to delineate the contribution of microtubules to the relaxation behavior of RVFW. After removing the microtubule network, RVFW elasticity and viscosity were reduced at the early diastolic strain level and in both directions. The reduction in elasticity was stronger in the longitudinal direction, whereas the degree of changes in viscosity were equivalent between directions. There was insignificant change in RVFW viscoelasticity at late diastolic strain level. Finally, the modeling showed that the tissue's relaxation strength was reduced by the removal of the microtubule network, but the change was present only at a later time scale. These new findings suggest a critical role of cytoskeleton filaments in RVFW passive mechanics in physiological conditions.