This paper investigates the influence of eccentricity on flow characteristics and particle migration in Couette geometries. The study involves numerical simulations using the recent frame-invariant model developed by Badia et al. [J. Non-Newtonian Fluid Mech. 309, 104904 (2022)]. The study begins with a two-dimensional analysis, focusing first on the Newtonian fluid in order to thoroughly characterize the specific properties of this flow configuration. Next, the impact of eccentricity on particle migration in an isodense suspension is examined by numerical simulations based on the experiments conducted by Subia et al. [J. Fluid Mech. 373, 193–219 (1998)]. Furthermore, the study is extended to include a full three-dimensional analysis of a dense suspension flow in an eccentric Couette geometry based on resuspension experiments conducted by Saint-Michel et al. [Phys. Fluids 31, 103301 (2019)] and D'Ambrosio et al.[J. Fluid Mech. 911, A22 (2021)]. The main objective of the latter study is to investigate the influence of eccentricity on the resuspension height and on the calculation of the particle normal stress in the vertical direction through the volume fraction profile analysis. Our results show that even minimal eccentricity can lead to significant changes compared to the centered case.