The advancement in the steering capabilities of fibre placement machines has improved the tailoring potential and therefore the design possibilities for composite structures. However, the larger design freedom leads to complex and non-convex design spaces. Finding the optimum solution thus becomes costly and challenging, specifically considering the non-linear coupling of thickness with the steering of the filaments or tows. Additionally, an accurate representation of the variable stiffness adds complexity to the modeling strategies, requiring additional refinement relative to constant-stiffness counterpart designs. Surrogate modeling and more exploratory optimization techniques make it possible to circumvent the higher execution time by using a limited set of high-fidelity model evaluations. This enables efficient and accurate exploration of the design space. Bayesian optimization techniques applies the surrogate model to offer strategic and probabilistic exploration of the design space and have demonstrated success in various fields. However, the application of Bayesian optimization schemes in structural optimization is in its nascent stage. The present thesis is a successful attempt that further pushes the application of Bayesian optimization for the lightweight design of variable stiffness cylinders. A novel finite element SC-BFSC is proposed for modeling and the computational efficiency for linear buckling analysis is investigated. The results showcase an enhanced computational efficiency with retained accuracy. Prior to optimization, a comprehensive Design of Experiment study is conducted, wherein different parameters and kernels were investigated for optimum performance. An optimization framework for the problem is proposed, utilizing the Gaussian process with Matern32 Kernel for regression model and a set of acquisition functions. The proposed optimization framework is implemented successfully and verified against a Genetic Algorithm(GA) based solution, which is an optimization method of proven success and robustness. The result obtained showcase the Bayesian optimization strategy's ability to identify comparable solutions at a fraction of the computation time required for the GA optimization in most cases. This study successfully demonstrates the Bayesian optimization's ability for designing lightweight variable stiffness cylinders, while providing a framework that is generally applicable in lightweight design of composite structures.