Unappalled is defined as not feeling shocked or surprised by something. Synonyms for unappalled might include unfazed, unaffected, undisturbed, unperturbed, calm, composed, collected, cool, and nonchalant. Other synonyms could include unalarmed, unimpressed, indifferent, phlegmatic, stoic, serene, and tranquil. These words all convey a sense of being unperturbed by some kind of stimulus, whether it be a tragic event or a startling development. When someone is unappalled, they are showing remarkable calmness and composure in the face of adversity, and any of these synonyms could help describe their demeanor.