Dissertation (MSc Statistics)The study deals with the analysis of a trend model on quarterly and yearly rainfall over Tanzania; conventionally and modern approach for the last 30 years. The yearly rainfall data from 1986 to 2016 was obtained from the Tanzania Meteorological Agency, Dar es Salaam, Tanzania. The rainfall data from representative stations in the homogeneous rainfall zones over Tanzania were analyzed for trends by graphical and statistical Methods. In order to achieve the main and specific objectives, the data were subjected to various analyses. The core methodology used in analysis of rainfall trends and variability over Tanzania were the time series analysis. The results from the study showed that there were trends in the rainfall data for all stations used. However the trends are not significant : In this study we fit a time series model that best describes the rainfall pattern of Tanzania country from the general ARIMA family and generate the values (p,d,q)(P,D,Q)s. The model that best fitted the Tanzania historical rainfall data was ARIMA (2, 1, 1) and SARIMA(0,0,0)(1,1,1). These models are used to forecast average expected yearly and quarterly rainfall statistics for four years. For verification and data fitting to the model, SPSS software was used. Model identification was by visual inspection of both the sample ACF and sample PACF to postulate many possible models and then use the model selection criterion of Residual Sum of Square (RSS),Akaike’s Information Criterion (AIC) complemented by the Bayesian Information Criterion (BIC), to choose the best model. We used the model to forecast rainfall for 2020 and the result compared very well with the observed empirical data for 2020 by Linear Regression Model (conventional model).