Advanced Grid Stiffened composite structures are desirable building components for space flight vehicles because they provide enhanced stiffness yet are relatively low-cost, long-lasting, and light-weight. Analysis of a grid stiffened structure presents significant challenges. The stiffener design is discrete and involves a set of stiffener orientations which complicates the solution process. Most optimization algorithms only provide a single global optimum, while a designer would want to obtain all of the local minima that have performance close to the global optimum. As a preliminary to the optimization analysis, the bending stiffness of grid stiffened cylinders will be modeled analytically with in-plane loads. The model developed in this paper will be used in further research with a hybrid optimization algorithm to conduct the optimization analysis.