Because there are so many different manufacturers producing yoga mats these days, it is important to look at the product specifications to see what kind of materials are going into yours.
In response to your question, there is no polyurethane in any of the yoga mats that we reviewed here today, however, some products may exist in which polyurethane might be a component.
As far as natural rubber, none of these mats utilize it as it is not the best material for a “travel-style” yoga mat, as heavy and bulky as it is.