This paper concerns computational response predictions when a tuned mass damper is intended to be used for the suppression of vortex shedding induced vibrations of e.g., a bridge deck. A general frequency domain theory is presented and its application is exemplified on a suspension bridge (where vortex shedding vibrations have been observed and where such an installation is a possible solution). Relevant load data are taken from previous wind tunnel tests. In particular, the displacement response statistics of the tuned mass damper as well as the bridge deck are obtained from time domain simulations, showing that after the installation of a TMD peak factors between three and four should be expected.