Let B be a Banach space, X be a stable B -valued random vector with exponent d∈(0,2), and P(·) be the distribution density of the norm of X. In this paper we study the question of the boundedness of P. In particular, we construct examples of a space B with a symmetric stable vector X with exponent d∈(1,2) with unbounded P and prove that if X is a nondegenerate strictly stable vector with exponent d∈(0,1), then P is bounded.