Beam-driven steady state Tokamaks of moderate size (R0=4.55 m) are analyzed by an optimizing beam current drive analysis code, which consistently includes MHD equilibrium, kink and ballooning stability analysis, bootstrap current, global power balance and toroidal momentum balance calculations. The maximum Q values attained are Q=7-9 with fusion powers of Pf=500-800 MW. L-mode confinement given by Kaye-Goldston scaling is sufficient to sustain steady state conditions. The Q value is nearly doubled due to the bootstrap current and the Ti>Te feature of beam-driven Tokamaks. The optimum beam energy is 1.0-1.2 MeV and the toroidal rotation effects are negligible.