This document summarizes a study that uses finite element analysis and Monte Carlo simulation to analyze the bending stress of hollow circular composite beams under random loading conditions. The study varies design parameters like beam length, radius, ply angles, elastic modulus, and force randomly within defined ranges. It analyzes the relationship between maximum bending stress and each parameter. Random optimization is then performed to determine a set of parameters that minimize bending stress. The best optimized set is proposed to reduce bending stress under different loading conditions.