This paper is to solve the problem of poor stability of bidirectional shaft pumps, under reverse and low-head condition. In this study, computational fluid dynamics (CFD) calculations are carried out and verified by model test, under four theoretical conditions: steady, unsteady, unidirectional, and bidirectional fluid–solid coupling. The S-shaped elbow of bidirectional pump was divided into four schemes according to the ratio b of the centerline's radius. The effects of b value on the efficiency and stability in the forward and reverse condition of the pump device were analyzed and compared. When b value was 0.75, the efficiency and stability of the pump device proved best. The frequency domain of pressure pulsation and dynamic stress of bidirectional pump under zero and design head condition was analyzed. It was found that the bidirectional pump had main frequencies corresponding to 10 and four times the rotation frequency of the runner (fn), for most working conditions. While there is a subfrequency of 14fn in zero head operation, which is similar to the natural frequencies of first- and second-order, calculated in the modal analysis. This may be the cause of the larger vibration of the bidirectional pump when it starts under the condition of zero head.