Sonication-assisted liquid-phase exfoliation of graphite makes facile, scalable, and low-cost graphene production possible, but there is little information about how sonication-related factors such as vessel diameter (D) and liquid height (H) affect this process and how to scale-up this technique. In this article, the dependence of the sonication-assisted few-layer graphene (FLG) production on D and H was investigated based on experiments and numerical simulation which was performed by finite element method to determine cavitation-related parameters. It was found that by essentially changing the cavitation phenomenon, D and H could critically affect the FLG concentration, FLG yield, injected power, and production efficiency. Combined experimental and simulational analyses reveal that though D and H can change both cavitation volume and cavitation volume fraction, it is the cavitation volume fraction that directly relates to the FLG concentration and production efficiency with a monotonically increasing trend, while the FLG yield and injected power are almost proportional to the cavitation volume, which in turn follows a linear increasing trend with the sample volume. The practical importance for industrial FLG production may lie in the following: (1) D and H should be carefully designed to obtain high cavitation volume fraction to gain high production efficiency and FLG concentration or output-input ratio and (2) large D, H, or sample volume is necessary for achieving large cavitation volume to enhance the FLG yield. Moreover, enhancement in pressure amplitude or cavitation intensity could also favor FLG production. These results have verified the importance of D and H which are often ignored when studying graphene production, and will provide important information on designing large-sized vessels for mass-producing graphene by sonication.