To solve the satisfiability (SAT) problem in propositional logic, many algorithms have been proposed in recent years. However, practical problems are often more naturally described as satisfying a set of first-order formulas. When the domain of interpretation is finite and its size is a fixed positive integer, the satisfiability problem in the first-order logic can be reduced to SAT. To facilitate the use of SAT solvers, this paper presents an algorithm for generating SAT instances from first-order clauses, and describes an automatic tool performing the transformation, together with some experimental results. Several different ways of adding formulas are also discussed to eliminate symmetries, which will reduce the search space. Experiments show that the algorithm is effective and can be used to solve many problems in mathematics and real-world applications.