en Seismic Geotechnique Seismic Geotechnique Research Paper Research Paper In this paper, an advanced formulation of time-domain, two-dimensional Boundary Element Method (BEM) with material damping is presented. Full space two-dimensional visco-elastodynamic time-convoluted kernels are proposed in order to incorporate proportional damping. This approach is applied to carry out site response analysis of viscoelastic topographic structures subjected to SV and P incident waves. Seismic responses of horizontally layered site, semi-circular canyons, slope topography and ridge sections subjected to these incident waves are analyzed in order to demonstrate the accuracy of the kernels and the applicability of the presented viscoelastic boundary element algorithm. The results show an excellent agreement with recent published results obtained in frequency domain. Also, the effects of different material damping ratios on site response are investigated. BEM, Visco-elastodynamic kernels, Time domain, Viscoelastic, Topography effects 26 44 http://ijce.iust.ac.ir/browse.php?a_code=A-10-544-2&slc_lang=en&sid=1 M. Afzalirad m.afzalirad@srbiau.ac.ir 180031947532846006315 180031947532846006315 No Science and Research Branch, Islamic Azad University M. Kamalian kamalian@iiees.ac.ir 180031947532846006316 180031947532846006316 Yes International Institute of Earthquake Engineering and Seismology (IIEES) M. K. Jafari jafari@iiees.ac.ir 180031947532846006317 180031947532846006317 No International Institute of Earthquake Engineering and Seismology (IIEES) A. Sohrabi-bidar sohrabi@khayam.ut.ac.ir 180031947532846006318 180031947532846006318 No University of Tehran