The present article focuses on the study of the transport characteristics of nickel hydrogen selective membranes (nickel industrial capillaries of various wall thicknesses). The experimental data on hydrogen fluxes through nickel capillaries depending on the membrane wall thickness, temperature, and hydrogen partial pressure were obtained. The highest value of the specific hydrogen flux is ∼0.09 ml·min−1·cm−2 is achieved at 750 °C, pH2.1 = 0.5 atm and the wall thickness of 84 μm. To accurately determine the kinetic parameters of the process of hydrogen transport (the effective activation energy and the pre-exponential factor) in nickel capillaries with a wall thickness of 147 ≤ h ≤ 84 μm, a previously developed mathematical model was used, which takes into account the geometric characteristics of tubular membranes. The results of computer simulation are compared with experimental data.