The accuracy of velocity measurements made using a monopole acoustic logging-while-drilling measurement (ALWD) tool are influenced by the eccentering of the tool due to complex drill string movements. We use the velocity of collar flexural mode (at the source frequency range) as a reference and propose a classification of fast formations into (1) fast-fast (FF) formations with compressional velocity significantly larger than the collar flexural velocity and (2) slow-fast (SF) formations with compressional velocity approaching that of the collar flexural velocity. We use a 3D finite difference method (FDM) to simulate the response of an eccentered monopole ALWD tool with different eccentering magnitudes (offsets) for the two types of formations to facilitate better interpretation of velocity measurements made in an actual drilling environment. We find that the collar extensional mode, existing in both centralized and eccentered tool cases, only affects the formation compressional wave measurement and can be eliminated by using an isolator. The collar flexural mode, which is a shear motion in the collar and can only be excited in a centralized tool by a dipole source, is also excited when a monopole tool is eccentered, and significantly affects the measurement of the compressional velocity in the SF formation and that of the shear velocity in the FF formation, even for small eccentering offsets. The uncorrected monopole ALWD tool thus provides unreliable formation velocities (either the compressional or shear velocities) in fast formations because of the significant influence of the tool offsets on the measurement. To minimize the influence of tool offset on the measurements, we compare the differences between the waveforms collected for different azimuths and tool offsets and the centralized monopole waveforms. Read More: http://library.seg.org/doi/10.1190/geo2016-0387.1