This paper aims to model and design a lightweight U-bracket for two degrees of freedom (DOF) mechanism used to carry a machine gun. The mechanism is called a weapon station or a gun turret and can be mounted on any mobile platform. Due to the movement of the platform and the gun recoil force, the gun turret is subjected to high disturbances. So, to get better performances in terms of distributed efforts, stability and precision, the mechanism has to be optimally designed. The trunnion axis offset corresponding to higher dynamic and structural performance was determined based on probabilistic analysis and finite element simulations. Then, the co-simulation between MATLAB and ANSYS Parametric Design Language (APDL) was performed to get the optimal shape of the U-bracket by minimizing its mass, and maximizing its first natural frequency subjected to maximum stress constraint. To solve this constrained optimization problem, the Multi-Objective Genetic Algorithm (MOGA) technique was used. Through numerical simulations, the proposed approach shows the ability to provide a generic methodology to design the U-bracket of a 2-DOF weapon station efficiently.