In the present study, a model is suggested to explain the course of spin transformation in crystals containing linear trinuclear iron(II) clusters as structural units. The energy spectrum of an isolated trimer is described with due allowance of the effects of the cubic crystal field formed by the nearest surrounding of each Fe^II ion as well as by consideration of intracluster interactions in the nearest neighbor approximation. The intercluster cooperative interaction promoting the spin transition is assumed to arise from the coupling of molecular modes with phonons, that is, a feature characteristic for molecular crystals containing as a structural element single spin-crossover ions or complexes formed by these ions. It is demonstrated that in dependence on the relative strengths of intra- and intercluster interactions, the trinuclear systems can exhibit a variety of different types of spin transitions and, namely, gradual, step-like transitions and those characterized by a hysteresis loop. The effects of external pressure on the spin transitions in crystals of trinuclear clusters are explored taking into account that pressure affects both the energy gap between the high-spin and low-spin states and the characteristic parameters of cooperative interaction. In the framework of the suggested model, the spin transformation in the Fe₃(bntrz)₆(tcnset)₆ compound is comprehensively explained. The model also allows a qualitative and quantitative reproduction of the temperature and course of the spin transition in this compound under applied pressure.