When a composite quantum state interacts with its surroundings, both quantum coherence of individual particles and quantum entanglement will decay. We have shown that under vacuum noise, i.e., during spontaneous emission, two-qubit entanglement may terminate abruptly in a finite time [T. Yu and J. H. Eberly, \prl {93}, 140404 (2004)], a phenomenon termed entanglement sudden death (ESD). An open issue is the behavior of mixed-state entanglement under the influence of classical noise. In this paper we investigate entanglement sudden death as it arises from the influence of classical phase noise on two qubits that are initially entangled but have no further mutual interaction.

5 pages, 1 figure