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In this thesis, a methodology has been proposed for strengthening of existing buildings for additional base shear demand and serviceability requirement using visco elastic dampers. Seismic zone map in Indian standard IS 1893 Part 1 2002 is being revised from time to time which leads to increase in elastic demands on existing buildings. Base shears for a typical low rise (three storey) and high rise (twenty storey) buildings for zone 2, zone 3, zone 4 and zone 5 for hard soil condition are estimated using seismic coefficient method and time history analysis with spectrum compatible acceleration. To study the effectiveness of the dampers, peak base shears, maximum displacements and accelerations are determined from the response of the damped buildings subjected to earthquake ground motion acceleration and the comparison has been made with those of the undamped buildings.