Constraint-based software specifications enable run-time monitoring to detect probable risk events and ensure the desired system behavior. SpecTRM-RL is a well-developed constraint-based specification method for computer-controlled systems. However, it is desirable to express constraints in familiar visual models. To provide better visualization and popularity, we developed methods to represent all the SpecTRM-RL constraint types in UML. We have also extended SpecTRM's constraints by adding relational and global constraints, and then expressed them in OCL. Safety verification of these specifications is also proposed. We developed a systematic way to construct fault trees for safety analysis based on UML diagrams. Due to the generality of UML as well as the defensive manner of constraints and fault tree analysis, our approach can be adapted for both general applications and safety-critical applications.