Hydrogen storage remains a major challenge for the large-scale implementation of hydrogen energy technologies. In this study, the hydrogen sorption behavior of Pd–Ti–Mg alloys synthesized by spark plasma sintering (SPS) was investigated using a combination of experimental characterization and numerical modeling. The phase composition and structural state of the synthesized material were analyzed by X-ray diffraction (XRD), while hydrogen absorption measurements were performed at different temperatures to evaluate its sorption behavior. A finite-difference numerical model was developed in MATLAB to simulate hydrogen diffusion, concentration distribution, thermally stimulated desorption, relaxation-stimulated gas evolution, pressure–composition–temperature (PCT) behavior, and hydrogen absorption–desorption kinetics. XRD analysis indicated a multiphase structure consisting predominantly of Pd₂Mg₅ and Pd₅Ti₃ intermetallic phases, together with residual Ti. Williamson–Hall analysis confirmed the nanocrystalline state of the synthesized material, with an average crystallite size of approximately 20–30 nm and microstrains of (3–5) · 10⁻³. The individual calculated crystallite sizes ranged from 18 to 35 nm, whereas the representative average value was approximately 20–30 nm. Experimental measurements demonstrated a pronounced temperature dependence of hydrogen uptake, with the highest measured hydrogen content reaching approximately 0.40 wt.% at 500 °C. Numerical simulations indicated that hydrogen transport is predominantly diffusion-controlled, resulting in a pronounced concentration gradient across the sample thickness. The thermally stimulated desorption model predicted a maximum hydrogen evolution rate of approximately 1.8 · 10⁻⁸ atoms s⁻¹ at 560–600 °C. The calculated PCT characteristics demonstrated a strong dependence of equilibrium hydrogen content on temperature and hydrogen pressure, with higher hydrogen contents predicted at lower temperatures and elevated pressures. Simulated absorption kinetics showed a rapid approach to hydrogen saturation within 10–30 s, whereas hydrogen desorption approached equilibrium within 80–120 s, depending on the applied pressure. The combined experimental and numerical results demonstrate the complementary roles of Pd-, Ti-, and Mg-containing phases in the hydrogen sorption behavior of the material, with Pd-containing intermetallic phases contributing to hydrogen dissociation and transport, while Ti- and Mg-containing phases contribute to hydrogen retention and storage. These findings demonstrate the potential of Pd–Ti–Mg-based intermetallic materials as candidate materials for solid-state hydrogen storage and related hydrogen-energy applications.