A one-dimensional model for FEL undulator is presented through a computer simulation program utilizing MATLAB 6.1. The FEL type was chosen to be amplifier with helical undulator and the input wave, which is required to be amplified, was chosen to be a laser wave. The input electron beam is uniform with number of electrons between 64 and 256 with initial phases uniformly distributed along the interval (0- 2?). The work focuses on the linear mode of operation, where the output power is proportional to the input power. During this work the electrons bunch evolution inside the undulator was studied by using two methods: the electron lines interception method and the 3D bunch evolution method. The results of the two methods were close to each other, where it was shown that the vast majority of the electrons tend to accumulate at the beginning and the end of the bunch. The effects of the undulator parameters on the output power gain were studied, where it was found that the gain of FEL depends on the square of the number of input electrons and linearly on the undulator length and period. Finally, it was found that the FEL gain depends on the break point value of the undulator magnetic field that decides whether the relationship between the gain and the magnetic field has inverse or direct proportionality.