We study a firm's optimal transshipment problem considering the impacts of setup costs for transshipment and demand distribution shapes. We assume that the demand follows a three-point distribution, which changes from a degenerate distribution, to a unimodal distribution, and to a bimodal distribution as the demand shape parameter increases. We find that as the demand shape parameter increases, the optimal transshipment strategy changes from no transshipment to transshipment, and finally to no transshipment. The firm would use two-way transshipment when the shape parameter is relatively small, while it would use one-way transshipment when the shape parameter is relatively large. When the optimal strategy is one-way transshipment, the transshipment direction depends on the contribution margin as well as the demand shape, when the difference between the two demand uncertainties is small. Our study of a dual-channel retail system shows that the additional benefit of two-way transshipment is negligible when there are many retail stores.