When it comes to describing someone or something that is unimpressible, there are a variety of synonyms to choose from. For example, you might describe someone as being unflappable, meaning that they remain calm and composed even in the face of excitement or shock. Alternatively, you might use the term unresponsive to suggest that the person or thing in question is simply not moved by what is happening around them. Other options include indifferent, uninterested, impassive, stoic, and apathetic. Regardless of which synonym you choose, the underlying message is clear - this person or thing is not easily impressed or swayed by external factors.