In the data-driven mechanics, the constitutive material modeling is eluded, and data are directly employed as an input for finite-element analysis instead. Therefore there is no need for a direct constitutive relationship. The data itself inhabits the material’s behavior as well as the material’s scattering due to imperfections or a varying composition. Material uncertainties, which generally need to be modeled, are here inhabited in the data. Our contribution focuses on using data-driven mechanics for cellular materials. Since experimen- tal data acquisition can be tedious, we suggest using numerical computations of representative volumes. In that way, the micromechanical behavior of the material can be employed to deduce homogenized data points. Here we focus on the modeling of polyurethane foam. Dependent on the manufacturing process and the composition of the constituents, the material properties such as density, pore distribu- tion, and structure of the material vary. To avoid fitting a material model for every case, we use stochastic representative volume elements (RVEs) to generate the data basis. A foam generator produces the RVEs with the desired properties, which are then subjected to some test loads to deduce homogenized data points. To not simulate each point individually, the database is constructed with the help of material properties such as linearity or isotropy. Finally, by means of numerical examples, data acquisition, preparation, and a multilevel solution strategy are discussed.