In most animal studies, the animal will go through stress and pain as a direct result of the experimentation on them with chemicals, diseases, etc., so there will be a level of stress and pain inherent to the study. Studies that receive funding from the NIH need to pass an ethics committee that consists of a variety of members that include people that work for the institution performing the study, as well as members of the general public that have no other connection to the institution (or even the scientific industry). They are there as a "proofreader" and to ensure that the protocol has as little pain and stress for the animals built into it as possible.
For example, I worked in a lab where we studied corneal herpes simplex virus infections, and the experiments that gave the most complete picture of what was going on were when we could do them in mice. So, we had to not only give the mice herpes in their eyes (which is not pleasant), but poke them with needles to anesthetize them and give them antibodies, plus the stress on the mice from handling them and eventually euthanizing them.
Just a snippet of some of the things that were required to be considered and addressed directly in the protocol:
What type of animal is being used for the study and why? Is it possible to use a "lower" animal and still attain accurate and precise data that tells the researcher what they need to know? Can we use a rat or mouse instead of a chimp? Can we use a zebrafish instead of a mouse? Can we use a worm instead of a zebrafish? Can we not use an animal and all and get good data from an in vitro study using cell cultures?
What guage needle is being used for injections? Is it both possible and practical to use a smaller gauge needle?
How many mice will share a cage of a given size?
How many mice are needed for the study? Too few would mean random anomalies could completely throw off your data, and then you just inflicted suffering on an animal for a bad study that didn't tell you exactly what was going on. How many is enough without being too many?
What time of day will the experiments be performed? How will the experiments and lighting in the room affect the animals' natural circadian rhythms?
What temperature will it be in the room where the animals are kept?
How often will experimenters be in the room disturbing the animals?
What types of anesthetics are being used, and at what dosing?
There are also pain studies that are dependent upon inflicting pain (we didn't do any of those). They're so that we have a better understanding of how pain works, or how effectively a new painkiller works. These have more rigorous and special considerations that they must pass.
So yes, the animals undergo stress and pain. No researcher that does medical studies on animals will try to argue otherwise. However, we either use animal studies or we jump straight from cell culture assays to human studies on medications, diseases, and chemicals. But, for as good as cell culture models and assays have become, they still don't give a complete picture of what is happening inside an animal. We can culture muscle cells to see the effect of a certain medication on them, but that won't tell us if your immune system or liver take that medication, digest it, and turn it into a form that is toxic to brain cells. So something that looks totally safe and effective in a cell culture may end up causing horrendous effects in a complete, living organism. In the end, it's necessary, but when there is an advance in the field and a new technique becomes available where animals are no longer needed for a certain type of study, researchers rejoice.