The subject of investigations is seismic input models for tuned mass damper designing. Some features of simulating design accelerograms for estimating seismic stability of a structure with a mass damper are considered. The method of accelerogram modeling, proposed by Dolgaya A.A., approved by the Building Ministry of Russian Federation and included and in the corresponding Recommendations in 1996, is considered as the basic one. In accordance with this method, an accelerogram is modeled by a sum of three damped sinusoids. The sinusoid frequencies are chosen as dangerous for the structure, and the amplitudes and damping parameters are chosen so that the kinematic and energy characteristics of the model input correspond to the actual ones. The main feature of MD designing is the presence of close frequencies, and the choice of a dangerous frequency is not unambiguous. Features of choosing a dangerous frequency and the influence of various characteristics of real accelerograms on the generated synthetic accelerogram are considered.