The nature and distribution of earthquake damage is strongly influenced by the response of soilsrnto cyclic loading. Design of geotechnical engineering problems that involve dynamic loading ofrnsoils and soil-structure interaction systems requires the determination of dynamic soil properties.rnThe response of soil to cyclic loading is determined mainly by the shear modulus and dampingrncharacteristics of the soil. In Ethiopia, areas close to the Ethiopian rift valley are prone torndamaging earthquakes. However, little experimental work has so far been done in assessing therndynamic properties of soils and only two researchers have attempted to experimentally measurerndynamic properties of red clay soils found in Addis Ababa.rnIn this thesis, the shear modulus and damping ratio values of soils commonly found in Hawassarnwere determined using cyclic simple shear testing machine on remolded samples. The tests werernconducted as a function of cyclic strain amplitude of 0.01 %, 0.1 %, 1 %, 2.5 %, and 5 % underrnthe axial pressures of 100 kPa, 250 kPa and 400 kPa. The test results revealed that the shearrnmodulus reduction values are in good agreement with well established literature values except atrnthe lowest strain level (0.01 %). The damping ratio values of the tests are generally lower thanrnthe literature values except at the lowest strain level (0.01 %). This indicates that, the testingrnconditions appear to have significant effect on the damping ratio values but little effect on thernshear modulus reduction values. Using the test results, the computed maximum shear modulus,rnGmax, values for the soils considered in this work are within the range of 31,734 kPa to 98,084rnkPa, which is acceptable for this soil type based on the literature.