Because flows in a stirred tank are complicated by rotating blades and baffles, the mechanism of fluid mixing is difficult to analyze. The pathlines of fluid particles in this system are characterized by unsteadiness, three-dimensionality and a lack of symmetry. However, the flow field does not necessarily involve the same complexity as the pathlines. In this study, we propose a simplified flow model of the complex flow motion in a stirred tanks, in which the flow velocities are expressed as a linear combination of elementary flows. By timing the parameters contained in the model equations, changing the combination and relative intensities of the components, we were able to simulate flows corresponding to various shapes, numbers and positions of blades and baffles. This simplified flow model is useful for finding the elementary flow essential to fluid mixing in a stirred tank and elucidating the mechanism of mixing.