In this paper, we study the problem of power allocation for streaming multiple variable-bit-rate (VBR) videos in the downlink of a cellular network. We consider a deterministic model for VBR video traffic and finite playout buffer at the mobile users. The objective is to derive the optimal downlink power allocation for the VBR video sessions, such that the video data can be delivered in a timely fashion without causing playout buffer overflow and underflow. The formulated problem is a nonlinear nonconvex optimization problem. We analyze the convexity conditions for the formulated problem and propose a two-step greedy approach to solve the problem. We also develop a distributed algorithm based on the dual decomposition technique, which can be incorporated into the two-step solution procedure. The performance of the proposed algorithms is validated with simulations using VBR video traces under realistic scenarios. Copyright © 2012 John Wiley & Sons, Ltd.