We present an efficient scheme to compute high-frequency seismograms (up to 10 Hz) for SH-waves in a horizontally stratified medium with the mode summation method. The formalism which permits the computation of eigenvalues, eigenfunctions and related integral quantities is discussed in detail. Anelasticity is included in the model by using the variational method. Phase velocity, group velocity, energy integral and attenuation spectra of a structure enable the computation of complete strong motion seismograms, which are the basic tool for the interpretation of near-source broad-band data. Different examples computed for continental structures are discussed, where one example is the comparison between the observed transversal displacement recorded at station IVC for the November 4, Brawley 1976 earthquake and synthetic signals. In the case of a magnitude M L =5.7 earthquake in the Friuli seismic area we apply the mode summation method to infer from waveform modeling of all three components of motion of observed data some characteristics of the source.