The uniaxial tensile modulus and strength of Alulight® foams are measured and simulated taking into account the non-uniform mass density distribution characterized non-destructively by X-ray computer tomography. The density mapping method is employed for the reconstruction of the hard and soft regions in the samples investigated. A finite element (FE)-model is introduced for simulations of the deformation of a continuum composed by domains of different local densities. Existing constitutive laws for cellular structures are incorporated for the numerical simulation of tensile deformation and the variance of the material parameters is determined with the aid of a scaling relationship. The experimental results for the stiffness, the ultimate strength, and the corresponding strain agree with the developed 3D FE simulations and are compared with the estimations according to scaling laws for uniform cellular structures. The non-uniformity of the material distribution affects the strength and the ductility significantly. Simulations taking this into account provide conservative property predictions. The calculated positions of local strain concentration correspond with the observed locations of crack initiation. The material modelling and the simulation of the elasto-plastic deformation up to damage are suggested for application to macroscopic components made of non-uniform cellular metals.