The vibratory punch problem for a viscoelastic half-space indented by a padded annular disk is investigated. By virtue of transform methods, the problem is formulated as a set of triple integral equations which are reducible to a Fredholm integral equation of the second kind. In the formulation, the response of a thin buffer which regularizes the load transfer to the semi-infinite solid is approximated via a plane stress-type solution. A set of numerical results is included to demonstrate the effect of padding characteristics on the dynamic system response. Apart from providing an interpretation tool for the nondestructive testing methods involving buffered annular loading systems, the present solution can be used as an effective approximation to the corresponding rigid-punch problem which has so far eluded a rigorous mathematical treatment.