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Bed mattresses made of polyurethane foam are becoming increasingly popular, and their surface design can be further improved by utilizing a high degree of design freedom in terms of their mechanical properties. This paper presents a technology for designing the surface shape of bed mattresses to enhance their functionality in the numerical analysing of mattress mechanics. In particular, it is a method using the elastoplastic constitutive equation, a common model for nonlinear deformation analysis, to compute the deformation behaviour of the mattress surface that has remarkable compressibility. In this study, an indentation test, which is one of the general methods used in material testing, was performed to investigate the deformation behaviour of polyurethane foam materials. The experiment was analysed using the elastoplastic constitutive model in the finite element method. The material parameters for the elastoplastic analysis are defined and applied to the simulations of the deformation behaviour of the mattress surface. From the finite element simulation results, it is found that the compressible deformation of the foam material can be evaluated using zero Poisson's ratio, which is typically positive for incompressible materials like metals.