The nonlinear, time dependent photon transport equations of Frantz and Nodvik, which describe the amplification of an optical pulse in an active medium, are modified to a simpler equation which describes only the amplification of energy. With this equation, the output energy of the high power YLF($Nd^{3+}$)-phosphate glass($Nd^{3+}$) laser system is calculated. When the stored energy density $E_{st}$ is 0.10J/$cm^3$, 0.16J/$cm^3$, 0.228J/$cm^3$, and 0.50J/$cm^3$, and with the assumption of uniform population inversion density, the final output energy of this laser system is 5. 38J, 176J, 317J, and 2834J, respectively. The gain saturation causes distortion of the output beam. This phenomenon is described in detail at the first three rod amplifier systems in the case of $E_{st}=0.228J/cm^3$. The peak current and decay time constant of the flashlamps, which are used to obtain population inversion in the active medium, are investigated. The flashlamp driving circuit which has optimum operational performance should have $\sqrt{LC}$ time about 100$\mu$sec.
