This article presents a staggered grid time-domain finite-difference (FD) program for the simulation of sH-wave propagation in a viscoelastic heteroge¬neous medium. The incorporation of realistic damping in FD program is based on a rheological model widely known as generalized maxwell body (gmB-EK). The accuracy of implementation of realistic damping is validated by comparing the numerically computed frequency dependent quality factors and phase velocity with the same computed using gmB-EK rheological model and the Futterman’s relationship. The accuracy was also validated by comparing the numerically com¬puted soil amplification at resonance frequency for different damping with the analytical solutions. The stability and grid dispersion are also studied in details.Prikazan je program konačnih razlika (FD) na razmaknutoj mreži u vremenskoj domeni za simulaciju rasprostiranja sH-vala u viskoelastičnom heterogenom sredstvu. Uključivanje realističnog prigušenja u program temelji se na reološkom modelu poznatom kao generalizirano maxwellovo tijelo (gmB-EK). Valjanost implementiranog prigušenja je potvrđena usporedbom numerički dobivenih frekventno ovisnih kvalitativnih faktora i fazne brzine s onima izračunatim gmB-EK reološkim modelom i korištenjem Futter¬manove relacije. Točnost je potvrđena i usporedbom numerički izračunate amplifikacije tla pri rezonantnoj frekvenciji za različito prigušenje s analitičkim rješenjima. stabilnost i disperzija mreže su također detaljno istraženi
