Side lobe level reduction is one of the most critical research topics in antenna arrays beamforming as it mitigates the interfering and jamming signals. In this paper, a hybrid combination between the Genetic algorithm (GA) optimization technique and the gauss elimination (GE) equation solving technique is utilized for the introduction of the proposed GA/GE beamforming technique for linear antenna arrays. The GA is chosen as it is a search-driven optimization strategy based on the concepts of genetic and natural selection. It is often used to identify optimal or near-optimal solutions to complex problems that would otherwise take a very long time to solve. The proposed technique estimates the optimum excitation coefficients and the non-uniform inter-elements spacing for a specific side lobe (SL) cancellation without disturbing the half power beamwidth (HPBW) of the main beam. Different size Chebychev linear antenna arrays are taken as simulation targets. The simulation results revealed the effectiveness of the proposed technique. Furthermore, the feasibility of realistic validations of synthesized arrays is demonstrated using the computer simulation technology (CST) microwave studio software package, which provides users with an optimized modeling environment and results in realizable and realistic designs.