Papaya fruit, widely consumed around the world, is mechanically and structurally affected by several enzymatic processes during ripening, where pectin methylesterase plays a key role. Hence, the aim of this work was to evaluate possible correlations among physicochemical changes, mechanical parameters, viscoelastic behavior, and enzyme activity of pectin methylesterase to provide information about the softening phenomenon by applying the Maxwell and Peleg models. Mechanical parameters were estimated by texture profile analysis, enzyme activity by Michaelis-Menten parameters, and viscoelastic behavior by relaxation test responses fitted to these models. The Maxwell model described properly mechanical changes during ripening, displaying a better adjustment (R2 > 0.97) than the Peleg model (0.80 < R2 < 0.84). Pearson correlation analysis (P ≤ 0.01) indicated an inversely proportional relation among firmness, total soluble solids, and the first elastic element of the Maxwell model. Besides, the PME Michaelis-Menten affinity constant showed a correlation between the first elastic element and the first viscoelastic element of the Maxwell model. Findings of this work pointed out that the first Maxwell elastic element could explain structural changes as papaya ripening advance, associated with pectin methylesterase activity, cell wall disruption, and cell assembling into the tissue. PRACTICAL APPLICATION: Mechanical and viscoelastic behavior of papaya fruit tissue were described by the Maxwell model associating both viscous and elastic elements to the softening process. The results provide background and practical knowledge to describe structural changes during the ripening process of papaya depending on its enzymatic activity. Outcomes could be further applied to understand changes in other fruits or food matrixes that soften during postharvest, storage, and food chain supply processes.