We describe a numerical study to quantify the influence of tool-eccentricity on wireline (WL) and logging-while-drilling (LWD) sonic logging measurements. Simulations are performed with a height-polynomial-adaptive (hp) Fourier finite-element method that delivers highly accurate solutions of linear visco-elasto-acoustic problems in the frequency domain. The analysis focuses on WL instruments equipped with monopole or dipole sources and LWD instruments with monopole excitation. Analysis of the main propagation modes obtained from frequency dispersion curves indicates that the additional high-order modes arising as a result of borehole-eccentricity interfere with the main modes (i.e., Stoneley, pseudo-Rayleigh and flexural). This often modifies (decreases) the estimation of shear and compressional formation velocities, which should be corrected (increased) to account for borehole-eccentricity effects. Undesired interferences between different modes can occur at different frequencies depending upon the properties of the formation and fluid annulus size, which may difficult the estimation of the formation velocities.