The optimal tuning of a mechanical system in terms of torsional dynamics is a very important function of the flexible shaft coupling, built in the system. Therefore, a flexible coupling with suitable dynamic properties has to be carefully chosen for each specific application. The main advantage of the pneumatic flexible shaft couplings, that is, torsional vibration tuners, developed at our department, is that we can easily regulate their dynamic properties, particularly their dynamic torsional stiffness during the operation of a mechanical system. In order to improve our pneumatic tuners in terms of better utilisation of their pneumatic flexible elements and achieving specific operational properties, two new pneumatic tuners with tangential arrangement of their pneumatic flexible elements were designed. The aim of this article was to introduce these new pneumatic tuners, protected by means of utility models, namely a tangential pneumatic flexible shaft coupling with axially deformed flexible elements and tangential pneumatic flexible shaft coupling with serial arranged flexible elements. Due to the fact that both mentioned pneumatic tuners are not yet