Abstract: Constraints involving Boolean and numerical variables are used widely, but are difficult to solve especially when they contain nonlinear numerical expressions. Many existing methods for solving such constraints are incomplete. A new method is presented in this paper to solve Boolean combinations of the nonlinear numerical constraints completely. This method combines the numerical methods and interval analysis together. It has been implemented in a prototype tool, and some experiments are made. The experimental results show that this method is effective, efficient, and complete.