In this thesis, we develop Bayesian methodology for univariate and multivariate categorical survey data. The Multinomial model is used and the following problems are addressed. Limited information about the design variables leads us to model the unknown design variables taking into account the sampling scheme. Random effects are incorporated in the model to deal with the effect of sampling design, that produces the Multinomial GLMM and issues such as model comparison and model averaging are also discussed. The methodology is applied in a true dataset and estimates for population counts are obtained