<p>Mechanical response of 12 different polyurethane (PU) foams, including both non-auxetic and auxetic variants, under cyclic compression tests was investigated. The foams were subjected to varying strain rates and two compression factors (~ 2 and ~ 3) during the auxetic conversion process. Auxetic foams exhibit higher compression strength and energy dissipation compared to conventional foams. The mechanical response is affected by the raw materials, additives like silver nanoparticles (SNP) and castor oil (CO) and the compression factor used for auxetic conversion. To model the behavior accurately, a visco-hyperelastic approach was employed, combining the modified Ogden hyperelastic model which includes a Poisson’s function and the hereditary integral model. MATLAB’s optimization routines were used to determine the hyperelastic and viscoelastic model parameters. The obtained experimental stress–strain curves were compared with the ones predicted by the models. The model predicted curves showed a good match with the experimental data for most of the foams. The model worked well for auxetic foams compared to conventional polyurethane foams. The ability of these models to predict the mechanical response of auxetic foams needs to be ascertained through finite element simulations corresponding to the experimental studies.</p> Graphical abstract <p></p>