Question: I have always known that rabbits are incapable of vomiting. However, recently, someone asked this question online, ‘why is my rabbit vomiting’. I got confused not knowing whether it is possible for them to throw up or not.
Answer: Rabbits cannot vomit. Most sources  concur on this fact and this is one of the reasons why they often suffer from intestinal blockages or furballs if they ingest their fur, unlike cats and dogs that do puke or upchuck.
It is also the same reason why they have gas problem which is often painful and signified by the various indications of pain in this pet.
Why don’t they throw up?
With a clear answer on whether bunnies do throw up or not, we need to look at some of the possible reasons why they cannot vomit, and they include the following.
They have a weak diaphragm
Their diaphragm with less muscular which would otherwise give them thrust to upchuck anything ingested. Most animals that throw up such as dog and cats often have muscular diaphragms.
Their stomach anatomy and structure
The structure of their stomach especially the cardia region which has thin non-glandular walls together with the cardiac sphincter add on to the reason why these pets do not vomit.
Also, the cardia is immobile and food movement is aided by bunny movements as well as the colon movement. This is how food is churned.
Therefore, it can be concluded that “the physiology of rabbit digestive system is such that rabbits are not able to vomit” 
Research on rodents , which do not also puke such as rats and mice have shown that when these rodents are given nauseating compounds to make them upchuck, there is a little mouth, no shoulder and throat activities which are associated with vomiting.
This can be used to conclude that, maybe rabbits too do not have brain circuits that are meant to trigger upchucking.
What about reported cases of a rabbit puking?
Whereas we might not be able to competently verify on the accuracy and authenticity incidents of some rabbit throwing that have been reported . There have been such reports.
In fact, there seem to be few incidences where this pet has been noted to vomit or this could have been confused with something else such as chocking or food aspiration into the airway and as the rabbit tries to cough it out, it was assumed he or she was throwing up.