Expansive soils have a special mineralogical characteristic which leads to swelling when exposed to moisture change. This behavior is due to the presence of considerable amount of montmorillonite clay mineral. Lightly loaded engineering structures such as pavements, single story buildings, railways and walkways may experience severe damages when they are constructed on such soils. Quantifying the swelling pressure for expansive soils caused by their expansion are essential in geotechnical engineering. Different researchers have developed an empirical relation for the estimation of swelling pressure from index properties of expansive soils for their locality. The formation and development of soil structure has very erratic nature and the swell pressure is dependent on the stress conditions, environmental factors and soil characteristics which vary from place to place, therefore equations developed for soils in one place may not work at all if tested on soils of other place of the same region. Hence specific models have to be developed for specific areas in order to give fair evaluations. As aresult new model is going to be determined for soils founed in Bahir Dar. To this regard, a series of laboratory tests were conducted on representative expansive soil samples. Laboratory tests such as free swell, specific gravity, particle size distribution, atterberg limits, natural moisture content, dry density and swelling pressure was conducted. Using index properties of soils as independent variable and swelling pressure as dependant variable, both linear and multiple linear regression analysis was undertaken by employing SPSS 2020 softwere. Accordingly the results of the statistical analysis show that good correlation does exist between index properties and swelling pressure of expansive soils. Using the measured swelling pressure and predicted swelling pressure, replacement depth to counterforce the swelling was calculated.