Electron beam parameters calculation results are presented and discussed for the 1.4 MeV electrostatic tandem accelerator, which is used in the Tel-Aviv University Free Electron Laser (TAU-FEL). Electron beam optics parameters including space charge effects were calculated for a beam line configuration, consisting of an electron gun, focusing solenoids, accelerating and decelerating sections, focusing quadrupole lenses and a wiggler. A new program for simulation of electron beam transport in the FEL ("ELOP") was developed recently at Tel-Aviv University (TAU). Equations of motion of an electron in the presence of magnetic and electric fields are solved numerically for different magnetic elements. The program was applied for simulation of electron beam transport in the TAU FEL. The results of the simulation provide guidelines for applying the appropriate currents to the quadrupole magnets along the beam line. A comparison of calculated and measured beam diameters is provided. Optimization problems of electron beam parameters are discussed.