Non-invasive evaluation of the Achilles tendon elastic properties may enhance diagnosis of tendon injury and the assessment of recovery treatments. Shear wave elastography has shown to be a powerful tool to estimate tissue mechanical properties. However, its applicability to quantitatively evaluate tendon stiffness is limited by the understanding of the physics on the shear wave propagation in such a complex medium. First, tendon tissue is transverse isotropic. Second, tendons are characterized by a marked stiffness in the 400 to 1300 kPa range (i.e. fast shear waves). Hence, the shear wavelengths are greater than the tendon thickness leading to guided wave propagation. Thus, to better understand shear wave propagation in tendons and consequently to properly estimate its mechanical properties, a dispersion analysis is required. In this study, shear wave velocity dispersion was measured in vivo in ten Achilles tendons parallel and perpendicular to the tendon fibre orientation. By modelling the tendon as a transverse isotropic viscoelastic plate immersed in fluid it was possible to fully describe the experimental data (deviation<1.4%). We show that parallel to fibres the shear wave velocity dispersion is not influenced by viscosity, while it is perpendicularly to fibres. Elasticity (found to be in the range from 473 to 1537 kPa) and viscosity (found to be in the range from 1.7 to 4 Pa.s) values were retrieved from the model in good agreement with reported results.