The paper presents a parametric study on the seismic response of bridge piers founded on gravity caissons. Despite the wide use of caissons in bridge engineering, until a few years ago this foundation typology has been less investigated than piles and shallow foundations in both static and dynamic field. In most of the published studies, the seismic design of bridge piers was carried out without accounting for soil-structure interaction or by means of an uncoupled approach in which the superstructure was solved independently from the soil-caisson subsystem. In this study, coupled systems made of soil, caisson, pier and deck were analyzed in the time domain by a 3D finite element approach, considering rigid and massive caissons embedded in linear viscoelastic soils. In addition to unravelling the contribution of kinematic and inertial interaction to the total response of the caisson-bridge-pier systems, the study focuses on a particular aspect of kinematic interaction, overlooked in practical design and in most of previous studies, represented by the kinematic bending arising in the bridge pier due to the pier-to-deck joint rigidity. For some critical combinations of soil compliance, caisson geometry, pier height and input motion characteristics, the pier-deck constraint could induce kinematic bending moments in the pier as important as the inertial ones. A closed-form equation was finally proposed to predict the maximum kinematic moment in the bridge pier as a function of the key model parameters identified through the parametric study.