In this paper, we investigate the problem of optimal power control for multiuser variable bit rate (VBR) video streaming in a cellular network with orthogonal channels. We adopt a deterministic model for VBR video traffic that incorporates video frame and playout buffer characteristics, and formulate a constrained stochastic optimization problem. We then develop a majorization-based solution approach. For the case of a single VBR video session with relaxed peak power constraint, we develop a power optimal algorithm with low complexity. We prove the power optimality of the proposed algorithm and the uniqueness of the global optimum, and demonstrate that the proposed algorithm is also smoothness optimal. For the case of multiuser VBR video streaming, we develop a heuristic algorithm that selectively suspends some video sessions when the peak power constraint is violated. In addition to the traditional VBR video streaming application, we also consider the case of interactive video streaming, and show that the proposed schemes can be easily adapted and applied. The proposed algorithms are evaluated with trace-driven simulations, and are shown to achieve considerable power savings and improved video quality over a conventional “lazy” scheme.