Basement excavation may induce unsymmetrical and highly skewed loadings and (or) stress changes in an existing tunnel, not only in the transverse, but also in the longitudinal direction of the tunnel. Although basement–tunnel interaction has attracted intense academic interest recently, it is often simply treated as a plane strain problem. In this study, however, based on a dimensional analysis of the governing parameters, two three-dimensional centrifuge tests were designed and carried out in dry sand to investigate the effects of a basement excavation on an existing tunnel located in two horizontal offsets in relation to the basement. In addition, a preliminary three-dimensional numerical analysis was conducted to back-analyse the centrifuge test and to investigate the effects of the tunnel cover-to-diameter and unloading ratios on the existing tunnel. For the specific conditions simulated and soil type tested, a maximum heave of about 0.07% of the final depth of the basement excavation (H e ) was induced in the tunnel that ran parallel to and beneath the basement. On the contrary, a maximum settlement of 0.014% H e was induced in the tunnel located at the side of the basement. For the former tunnel, the influence zone by the basement excavation on vertical tunnel displacement along the longitudinal direction was 1.2L (basement length). By inspecting the measured strains in the longitudinal direction of the existing tunnel, it was found that the inflection point, where the shear force is at a maximum, was located at 0.8L away from the basement centre. Due to stress relief from the basement excavation, the tunnel located directly beneath the basement was vertically elongated, but the one that lay at the side of the basement was distorted. A preliminary numerical parametric study found that tunnel heave decreased as the cover-to-diameter ratio increased, but at a reduced rate.