Abstarct: The popular model for spatial count responses in finite populations is constructed baxsed‎ ‎on binomial distribution‎. ‎In many applications‎, ‎due to overdispersion problem‎, ‎to use binomial distribution is not appropriate and can result in inefficient inferences regarding the estimation of parameters and spatial prediction‎. ‎In order to eliminate the defects of a binomial model‎, ‎an alternative approach for modeling spatially correlated proportions is to use a beta-binomial distribution‎. ‎The flexibility of beta-binomial distribution could make it the first choice for modeling overdispersed count responses in finite populations‎. ‎‎‎In this thesis‎, ‎we describe the spatial prediction of rates by using the flexible beta-binomial model and generalize it for spatial analysis of lattice data in the frxamework of Bayesian inference. We ‎‏‎a‎lso‎ demonstrate its efficacy by a simulation study‎. ‎To evaluate the performance of this model‎, ‎we analyze two real data sets including the number of rainfall days in Semnan province‎, ‎Iran and the number of people with gastric cancer in Guilan province‎, ‎Iran.