Since different X-ray tomographic techniques offer advantageous characteristics, they frequently complete or even replace standard methods based on acoustic emission, thermography and ultrasonic. Especially the detection and evaluation of voids and cellular structures can be performed with a resolution of up to 1 μm and 3D visualization. Within this paper, a novel in situ CT device is used to perform compression tests on closed-cell polymeric foams with a defined foam density. Next to the determination of the cell structure with consideration of the pore size distribution and their morphology, the elastic compression behaviour is investigated. Following the analysis of the foam structure, the implementation of an implicit Finite element model is developed based on computer tomographic scans. By the introduction of a phase field function to implicitly describe the foam structure, technical difficulties associated with meshing the complex structure can be avoided and the equations to describe the deformation behaviour are effectively solved on high performance computers. Beyond that, the results gained by the in situ CT device help to adapt and complete the currently available elastic deformation models and therefore offer the opportunity to predict the material behaviour for various load scenarios of polymeric foams.