Let q be an odd prime, and let Gn(q) denote one of the finite classical groups—namely, the general linear, unitary, symplectic, or orthogonal group—of rank n over the field GF(q) with q elements. Given an integer M≥2, an element g∈Gn(q) is said to be a root of identity if gM=1. In this article, we derive generating functions for the probability that a randomly chosen element of Gn(q) is an M-th root of identity. Our results depend on the specific types of irreducible factors that appear in the factorization of the polynomial xM-1 over GF(q).