In this study, the combination of dimensional analysis (DA) and analysis of variance (ANOVA) was used to predict the volumetric mass transfer coefficient (k(L)a) values under different operating conditions for orbitally shaken bioreactors (OSRs) with different filling volumes. It was found that Reynolds number and the interaction between Froude number and geometric number have the largest impact on k(L)a with impact indexes of 7.41 and 7.50, respectively. Moreover, the volume number has the largest negative impact on k(L)a, with an impact index of-5.34. Thus, an effective way to increase the oxygen supply is by increasing the shaking speed and shaking diameter or decreasing the vessel diameter. However, cell cultivation with a higher filling volume will have an increased risk of oxygen scarcity. Therefore, with the help of the k(L)a prediction model, a suitable operating condition can be determined effectively and easily.