Several approaches to measure similarity between UML models have been proposed in recent years. However, they usually fall short of what was expected in terms of precision and sensitivity. Consequently, software developers end up using imprecise, similarity-measuring approaches to figure out how similar design models of fast-changing information systems are. This article proposes UMLSim, which is a hybrid approach to measure similarity between UML models. It brings an innovative approach by using multiple criteria to quantify how UML models are similar, including semantic, syntactic, structural, and design criteria. A case study was conducted to compare the UMLSim with five state-of-the-art approaches through six evaluation scenarios, in which the similarity between realistic UML models was computed. Our results, supported by empirical evidence, show that, on average, the UML-Sim presented high values for precision (0.93), recall (0.63) and f-measure (0.67) metrics, excelling the state-of-the-art approaches. The empirical knowledge and insights that are produced may serve as a starting point for future works. The results are encouraging and show the potential for using UMLSim in real-world settings.