One of the causes of death of patients infected by SARS-CoV-2 is the induced respiratory failure caused by excessive activation of the immune system, the so-called "cytokine storm", leading to damage to lung tissue. In vitro models reproducing various stages of the disease can be used to explore the pathogenetic mechanisms and therapeutic approaches to treating the consequences of a cytokine storm. We have developed an in vitro test system for simulating damage to the pulmonary epithelium as a result of the development of a hyperinflammatory reaction based on the co-cultivation of pulmonary epithelial cells (A549 cells) and human peripheral blood mononuclear cells (PBMC) primed with lipopolysaccharide (LPS). In this model, after 24 h of co-cultivation, a sharp decrease in the rate of proliferation of A549 cells associated with the intrinsic development of oxidative stress and, ultimately, with the induction of PANoptotic death were observed. There was a significant increase in the concentration of 40 cytokines/chemokines in a conditioned medium, including TNF-α, IFN-α, IL-6, and IL-1a, which corresponded to the cytokine profile in patients with severe manifestation of COVID-19. In order to verify the model, the analysis of the anti-inflammatory effects of well-known substances (dexamethasone, LPS from Rhodobacter sphaeroides (LPS-RS), polymyxin B), as well as multipotent mesenchymal stem cells (MSC) and MSC-derived extracellular vesicles (EVs) was carried out. Dexamethasone and polymyxin B restored the proliferative activity of A549 cells and reduced the concentration of proinflammatory cytokines. MSC demonstrated an ambivalent effect through stimulated production of both pro-inflammatory cytokines and growth factors that regenerate lung tissue. LPS-RS and EVs showed no significant effect. The developed test system can be used to study molecular and cellular pathological processes and to evaluate the effectiveness of various therapeutic approaches for the correction of hyperinflammatory response in COVID-19 patients.