This work is integrated in the general schedule of activities aiming the design and setting up a Linear Electron Accelerator at the Brazilian center of Physical Research. The Linear Accelerator will provide a final energy of 50 MeV. The energy spectrum of such a device, and the electron capture efficiency of the wave are conditioned to the previous determination and optimization of the axial focusing conditions. These conditions will determine the parameters of the first accelerating unit, wich is designed to collect the injected electrons and take them to the ultra-relativistc region bunching them simultaneously by phase and by energy levels. It is the main purpose of this thesis to solve the problem of focusing, within certain conditions imposed on some parameters by other aspacts of the project. The work comprises the analysis of the problem, its adaptation to electronic computing and the numerical variation of the parameters, together with the plotting and interpretation of the curves, to choose the most convenient directions of change to adapt on the parameters, to attain optimization. The text goes as far as comparing the theoretical predictions with the measured performance of the bunching unit, designed and built as prescribed in this thesis. As a second object, with the same procedure, we studied the design of a pre-buncher, acting on velocity-modulation, to improve the electron capture efficiency of the bunching unit mentioned above.