Hydrogen as a versatile energy carrier continues to attract research attention in the field of applied chemistry. One of the fundamental issues on the way to hydrogen economy is the difficulty of hydrogen storage. Physical adsorption of hydrogen in pores is a feasible and effective method of hydrogen storage. Among existing hydrogen-adsorbing materials, carbon nanostructures possess a number of advantages due to their high adsorption capacity, significant strength and low weight. In this work, we use the modern methods of quantum chemistry (DFT, SAPT0 and IGM) to study the adsorption of molecular hydrogen in a series of simulated slit-like carbon micropores with a distance between the walls of d = 4–10 Å, including the introduction of an H2 molecule into a pore, filling pores with these molecules and investigating the interactions between H2 molecules inside the pores. It was found that, depending on the value of parameter d, adsorbed hydrogen molecules form one (d = 6, 7 Å) or two layers (d = 8, 9, 10 Å) inside the pore. At the same time, for pores with small d values, high potential barriers to the introduction of H2 into a pore were observed. The decomposition of the interaction energy into components showed dispersion interactions to make a major contribution to the energy of attraction (72–82%). Moreover, an increase in the number of H2 molecules adsorbed in the pore decreases the significance of dispersion interactions (up to 61%) and increases the contribution of electrostatic and induction interactions to intermolecular attraction. Gravimetric density (GD) values were determined for pores with d = 6, 7, 8, 9, 10 Å, comprising 1.98, 2.30, 2.93, 3.25 and 4.49 wt%, respectively. It is assumed that the revealed peculiarities of hydrogen adsorption in pores will contribute to the use of carbon porous structures as a medium for hydrogen storage.