In short, yes, Elmer’s glue is vegan.
All of Elmer’s glues are made synthetically, mostly from petroleum products.
You can find this statement on Elmer’s FAQ:
No, Elmer’s does not use animals or animal parts to make glue. Our products are made from synthetic materials and are not derived from processing horses, cows or any other animals.
While it’d be nice not to rely on oil for environmental reasons, it’s considered vegan by the vast majority of vegans.
Why Is There a Cow on the Label?
It seemed weird to me that there was a cow in Elmer’s logo so I looked into it.
Elmer’s glue was originally made by Borden, a company that primarily made dairy products.
The original glues also contained casein, which is one of the main proteins found in milk.
Note that the glue hasn’t contained dairy products for a long time.
Even though Elmer’s glue spun off and was acquired by multiple companies since then, the cow logo has stuck.