Computational thinking (CT) has attracted significant interest among many educators around the globe. Despite this growing interest, research on CT and programming education in elementary school remains at an initial stage. Many relevant studies have adopted only one type of method to assess students' CT, which may lead to an incomplete view of student development on CT, while other studies employed small sample sizes, which may increase the chance of assuming a false premise to be true. Moreover, conventional programming courses typically have two limitations (e.g., limited student active learning and student low engagement). Given these gaps, this study investigates the effects of a theory-based (5E framework) flipped classroom model (FCM) on elementary school students' understanding of CT concepts, computational problem-solving performance, and perceptions of flipped learning. To achieve this, a pretest-posttest quasi-experimental study was conducted in a rural elementary school, including 125 students in the experimental group and 122 students in the control group. The results showed that the 5E-based FCM significantly improved student understanding of CT concepts and computational problem-solving abilities. The results also revealed positive student perception toward the FCM. The benefits and challenges of the 5E-based FCM are discussed.