Inspired by the animal upper digestion tract, a strategy of developing soft-elastic reactors (SERs) for potential industrial usage has evolved, and is under the framework of bio-inspired chemical engineering. In our laboratory, two basic reactor categories have been experimented upon to explore the parameters influencing SER performance: vertical and horizontal cylindrical reactors. Different from the traditional rigid reactors equipped with solid agitators, SERs mainly triggers mixing through the movement of its elastic wall. The mechanisms of SERs are, however, not yet fully understood due to the limitations in the laboratory work in scale and in the diversity of the working conditions. For the first time we present a numerical study on the mixing behaviour of an SER to reveal its special characteristics as an alternative mixing method difficult to show in laboratory. Two-dimensional situations are analyzed numerically with a successful implementation of a moving mesh method in ANSYS Fluent. The approach allows versatile movement of the reactor wall to be effectively simulated. Systematic investigations were then carried out to investigate the effects of two chosen wall motion modes. The effects of such motion modes have been demonstrated through tracking the evolutions of the flow fields. This work shows room for potential improvements of SERs by devising different wall movements.