The hydrogenation of trans,trans-muconic acid was investigated on a Pt/C 5% (wt) catalyst in a batch slurry reactor at constant hydrogen pressure (4 bar) and temperature (323, 333 and 343 K), with the purpose of developing a kinetic model able to predict conversions and product distributions. A dual-site Langmuir−Hinshelwood−Hougen−Watson (LHHW) model with hydrogen dissociation provided good fitting of the experimental data. The model parameters were regressed by robust numerical methods to overcome the computational challenges of the model parameters’ collinearity. Different reaction mechanisms were tested; the best model involved two subsequent hydrogenation steps. The first step yielded from trans,trans-muconic acid a monounsaturated intermediate (trans-2-hexenedioic acid), which was further hydrogenated to adipic acid in the second step. The intermediate was subjected to an equilibrium isomerization with cis-2-hexenedioic acid. The activation energy values and the rate constants were calculated for the reactions, providing the first reference for trans,trans-muconic acid hydrogenation.