Abstract The complete blocked dynamic stiffness matrix of a long rubber bush mounting of particular interest for noise abatement is examined by an analytical model, where influences of audible frequencies, material properties, bush mounting length, and radius, are investigated. The model is based on the dispersion relation for an infinite, thick-walled cylinder with arbitrary boundary conditions at the radial inner and outer surfaces; yielding the sought stiffness matrix, including axial, torsional, radial, and tilting stiffness. A nearly incompressible material model is adopted, being elastic in dilatation while displaying viscoelasticity in deviation. The applied deviatoric Mittag-Leffler relaxation function is based on a fractional standard linear solid, the main advantage being the minimum number of parameters required to successfully model the rubber properties over a broad structure-borne sound frequency domain. The dynamic stiffness components display a strong frequency dependence at audible frequencies, resulting in acoustical resonance phenomena, such as stiffness peaks and troughs. The low-frequency stiffness asymptotes of the presented model are shown to agree with those of static theories.