Xanthan gum is commonly used in the pharmaceutical, cosmetic, and food industries. However, there have been no studies on utilizing this natural biopolymer as a foam material in the insulation and packaging sectors, which are large markets, or modeling it using an artificial neural network. In this study, foam material production was carried out in an oven using different ratios of cellulose fiber and xanthan gum in a 5% citric acid medium. As a result of the physical and mechanical experiments conducted, it was determined that xanthan gum had a greater impact on the properties of the foam material than cellulose. The densities of the produced foam materials ranged from 49.42 kg/m3 to 172.2 kg/m3. In addition, the compressive and flexural moduli were found to vary between 235.25 KPa and 1257.52 KPa and between 1939.76 KPa and 12,736.39 KPa, respectively. Five machine-learning-based methods (multiple linear regression, support vector machines, artificial neural networks, least squares methods, and generalized regression neural networks) were utilized to analyze the effects of the components used in the foam formulation. These models yielded accurate results without time, material, or cost losses, making the process more efficient. The models predicted the best results for density, compression modulus, and flexural modulus achieved in the experimental tests. The generalized regression neural network model yielded impressive results, with R2 values above 0.97, enabling the acquisition of more quantitative data with fewer experimental results.