It is known that American English /r/ can be produced as a retroflex or bunched /r/, but it can be challenging to teach students how to articulate both. We already developed a physical model for retroflex /r/ and demonstrated that the model produces the /r/ sound. However, almost no studies have reported a physical model for bunched /r/. We developed a new physical model using sliding blocks for the lips and tongue to help teach students how to produce bunched /r/. We recorded several sets of sounds produced by the models, analyzed the output signals, and used them for perceptual experiments. Acoustic analysis and perceptual experiments confirmed that the retroflex and bunched /r/ models produced clear American /r/ sounds, and that the narrow constriction placed between 5–7 cm from the lips seems to be the key in producing these sounds. Furthermore, bunched /r/ with lip rounding produced the most clear /r/ sound. Both models are helpful for practicing pronunciation because learners can readily see there are two ways to produce /r/, they can see and alter the tongue position manually, and they can hear the output sounds.