The ionosphere, also known as the ionized part of the upper atmosphere, is believed to vary as a function of di erent parameters such as solar and geomagnetic activities. One of the peculiar parameters that describes the variability of the ionosphere is its total electron content (TEC). This thesis focuses on modeling and predicting the variability of the daily and hourly vTEC as a function of F10.7 ux and storm time index (Dst) using multivariate quadratic modeling over Bahir Dar, Ethiopia. The analysis was done for 2010-2014 vTEC in both short-and long-term data set. From the modeling, we could infer both the linear and non-linear trends of the TEC as a function of F10.7 and Dst. The previews studies have reported both linear and non-linear trends of TEC variation. It means that there is no conclusive report on linear or non-linear dominancy of TEC variation with respect to solar and geomagnetic indices. We have also predicted the daily vTEC for each year under consideration. Thus, the analysis depicted that such a mixed trend of the vTEC variation is persistently occurring in both modeling and prediction aspects of the work. The deviation between the modeled vTEC and the observation has a clear daily and seasonal variations. Speci cally, we could observe high deviation during equinox than solstice seasons. Both the short-term and long-term analysis of the modeling depicted that the linear variation of vTEC as a function of F10.7 and Dst is more dominant than the non-linear variation. We have observed that on average, 70% of the variation of vTEC could be explained by the proposed multivariate quadratic model.