The present work addresses a stochastic computational solution to define the property closures of polycrystalline materials under uncertainty. The uncertainty in material systems arises from the natural stochasticity of the microstructures as a result of the fluctuations in deformation processes. The microstructural uncertainty impacts the performance of engineering components by causing unanticipated anisotropy in properties. We utilize an analytical uncertainty quantification algorithm to describe the microstructural stochasticity and model its propagation on the volume-averaged material properties. The stochastic solution will be integrated into linear programming to generate the property closure that shows all possible values of the volume-averaged material properties under the uncertainty. We demonstrate example applications for stiffness parameters of α-Titanium, and multi-physics parameters (stiffness, yield strength, magnetostrictive strain) of Galfenol. Significant differences observed between stochastic and deterministic closures imply the importance of considering the microstructural uncertainty when modeling and designing materials.