We study the problem of generating a database and parameters for a given parameterized SQL query satisfying a given test condition. We introduce a formal background theory that includes arithmetic, tuples, and sets, and translate the generation problem into a satisfiability or model generation problem modulo the background theory. We use the satisfiability modulo theories (SMT) solver Z3 in the concrete implementation. We describe an application of model generation in the context of the database unit testing framework of Visual Studio.