The mechanism of the intermolecular photoinitiated hydrogen transfer in fluorene crystal doped with acridine molecules is studied theoretically. For this reaction, extensive experimental data in a wide interval of temperatures and pressures are available in the literature. Computations of energetics for this reaction with the explicit account of the crystalline environment are performed at atmospheric pressure, and also at 10 and 20 kbar. Parameters of the fluorene crystal lattice are reported as functions of pressure. The reaction model considers a large cluster of crystalline lattice arranged around the reaction pair; it includes three coordination spheres and its structure depends on pressure. The interaction inside the chemical subsystem is calculated by a semiempirical quantum-chemical method (PM3); its interaction with the crystalline environment is treated in terms of the atom-atom scheme. Studies of the potential energy surface (PES), as a function of pressure, showed that the tunneling transition of H-atom is essentially two-dimensional. Other modes that undergo a significant rearrangement and determine the reaction mechanism are revealed and investigated. The mechanism of multidimensional tunneling is discussed, and the computational scheme aimed at estimating the corresponding rate constant is outlined. It includes a computation of special PES cross sections providing relatively low effective potential barriers during the tunneling. The main visible effect of pressure on the PES is a significant decrease of equilibrium distances between reactants, promoted by increasing pressure. This results in decreasing the effective tunneling barriers along the reaction path and accelerating the reaction.