A box particle filtering algorithm for nonlinear state estimation based on belief function theory and interval analysis is presented. The system under consideration is subject to bounded process noises and Gaussian multivariate measurement errors. The mean and the covariance matrix of Gaussian random variables are considered bounded due to modeling errors. The belief function theory is a means to represent this type of uncertainty using a mass function whose focal sets are intervals. The proposed algorithm applies interval analysis and constraint satisfaction techniques. Two nonlinear examples show the efficiency of the proposed approach compared to the original box particle filter.