Finite element analysis (FEA) is widely used in design of metamaterials to predict the mechanical behavior as a function of design variables such as geometry and material choice. While FEA modeling is mature, there are numerous modeling decisions that influence the reliability and outcomes of the simulation, especially for large material deformation and highly non-linear behaviors such as plasticity and buckling. These decisions become sources of epistemic uncertainty that propagate onto simulation outcomes and thus potentially affect designs. This thesis investigates the impact of two uncertainty sources that are especially relevant in studying buckling -- geometric imperfections and frictional interactions -- on a honeycomb-based cellular material. FEA package Abaqus is selected here and Python scripting is developed to achieve the FEA implementation and design automation. Uncertainty is characterized and quantified based on a large computational experiment, and the impact of the uncertainty on a set of simple robust design optimization and Bayesian optimization problems is illustrated. The results show that, combined, both factors introduce significant variability (up to 20%) in the mechanical response of the material, and consequently lead to changes (up to 10%) of the optimum design in a robust design optimization framework. This study suggests that ignoring these sources of uncertainty may lead to suboptimal designs for this class of material design problems. The methodology and codes developed in this thesis can be used to further explore the mechanical properties of metamaterials and facilitate material design.