The biological feature you're looking for is called segmentation.
Arthropod exoskeletons have very defined functional units broken down into groups called tagma. These tagma are groups of segments such as the thorax, the head, the abdomen, etc. Each of these groups are connected by joints.
After all, the word arthropoda means "jointed legs."
It doesn't necessarily have to be an insectoid creature but insects are among the arthropods along with other creatures like crustaceans and arachnids. The material chitin (which is a polymer) connects the joints in these creatures, and it's noted for being very flexible and durable.
In regards to your flexibility in the torso region, I found in New Zealand Journal of Zoology (1986) a detailed maneuver of a female jumping spider called the twist lunge.
This usually happened when the female's abdomen was rotated and the male either had his palp engaged or was scraping with his palp. The female then suddenly twist lunged by rotating her cephalothorax toward the male (i.e., moving her cephalothorax into alignment with her abdomen) simultaneously making scooping motions with her legs, and moving her extended fangs toward the male.
Flexibility as described above is something you want to look for when trying to make creatures like this, since it utilizes anatomical terms of motion (Flexion, abduction, elevation, rotation, etc.)