Automatic Test Pattern Generation (ATPG) is one of the core algorithms in testing of digital circuits and systems. Due to recent advances in algorithms to solve Boolean Satisfiability (SAT), there is a renewed interest in SAT-based ATPG. While the early approaches only used two-valued logic, modern tools have to use multiple values to model unknown values and tri-state elements for buses. In this paper we present a detailed study on how to chose the multi-valued encoding for SAT-based ATPG. The techniques have been implemented and evaluated on large industrial benchmarks.