The modal frequencies and bending mode shapes of a freely supported tapered violin bow are investigated by finite element analysis and direct measurement, with and without tensioned bow hair. Such computations are used with analytic models to model the admittance presented to the stretched bow hairs at the ends of the bow and to the string at the point of contact with the bow. Finite element computations are also used to demonstrate the influence of the lowest stick mode vibrations on the low frequency bouncing modes, when the hand-held bow is pressed against the string. The possible influence of the dynamic stick modes on the sound of the bowed instrument is briefly discussed.