Final answer:
The buccinator muscle is responsible for compressing the cheeks when performing actions such as whistling, blowing, and sucking on a straw, as well as aiding in the chewing process.
Step-by-step explanation:
The muscle that compresses your cheeks when you whistle or blow is the buccinator muscle. This relatively large muscle of facial expression is palpable in your cheek wall. The buccinator muscle is responsible for lateral movement of the cheeks, such as when you are sucking on a straw or blowing.
Besides these actions, it plays a crucial role in the process of chewing by keeping the food within the oral cavity. When eating, notice how the buccinator muscles actively contract to prevent food from falling out of your mouth. In addition to the buccinator muscle, other facial muscles such as the orbicularis oris regulate what enters and leaves the mouth, and the masseter plays a major role in the chewing process by elevating the mandible.