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The length of suction caisson anchors has been increasing to support increasing dimensions and weight of floating facilities, which necessitates employing horizontal ring stiffeners at intervals along the inner wall of the thin skirt of caissons to ensure structural integrity. The addition of these stiffeners has created significant uncertainties regarding soil flow mechanisms, in particular soil heave inside the caisson, which may reduce the caisson final penetration depth and influence the process of installation due to the need to avoid inside soil suction in the pumping equipment. This paper reports results of large-deformation finite element (LDFE) analyses investigating soil heave inside stiffened caissons during installation in nonhomogeneous clay deposits, with the corresponding evolution of soil flow mechanisms and penetration resistance profiles reported by Zhou et al. in 2016. The LDFE analyses have simulated continuous penetration of stiffened caissons from the seabed surface. A detailed parametric study has been undertaken, exploring the relevant range of soil strength nonhomogeneity and normalized strength, stiffened caisson geometry, soil effective unit weight, and caisson roughness. Of particular interest is the influence of stiffeners on soil heave and potential penetration refusal. The results have been validated against previously published centrifuge test data in terms of soil heave and penetration resistance profile, with good agreement obtained. It is shown that the soil normalized strength at the mudline and its nonhomogeneity, caisson diameter relative to the sum of skirt thickness and stiffener width, and caisson penetration depth have significant influence on the inner soil heave and its profile across the caisson radius. An expression, based on the LDFE results is proposed to predict the maximum inner soil heave during installation of stiffened caissons in the field.