Regular approximation is a well-known and useful analysis technique for conventional logic programming. Given the existence of constraint solving techniques, one may wish to obtain more precise approximations of programs while retaining the decidable properties of the approximation. Greater precision could increase the effectiveness of applications that make use of regular approximation, such as the detection of useless clauses and type analysis. In this paper, we introduce arithmetic constraints, based on convex polyhedra, into regular approximation. In addition, Herbrand constraints can be introduced to capture dependencies among arguments.