AbstractAn approximate analytical solution is presented for torsional vibrations of footings partially embedded into a semi‐infinite medium or a stratum. Simple formulas derived for pure torsional motion make it possible to apply a correction for the effect of embedment to the known solutions of surface footings. The solution completes an approach to the analysis of all modes of footing vibrations, including the coupled modes. The approach to coupled modes is illustrated by the solution of coupled response involving horizontal translation, rocking and torsion. Formulas are presented for stiffness and damping coefficients that can be used in the analysis of embedded footings or structures supported by such footingsField experiments were conducted with concrete footings featuring circular, square and rectangular bases and variable embedment depths. The experimental results were compared with theoretical predictions of pure torsional vibration