Plane beds develop under flows in fluvial and marine environments; they are recorded as parallel lamination in sandstone beds, such as those found in turbidites. However, whereas turbidites typically exhibit parallel lamination, they rarely feature dune-scale cross-lamination. Although the reason for the scarcity of dune-scale cross-lamination in turbidites is still debated, the formation of dunes may be dampened by suspended loads. Here, we perform, for the first time, linear-stability analysis to show that flows with suspended loads facilitate the formation of plane beds. For a fine-grained bed, a suspended load can promote the formation of plane beds and dampen the formation of dunes. These results of theoretical analysis were verified with observational data of plane beds under open-channel flows. Our theoretical analysis found that suspended loads promote the formation of plane beds, which suggests that the development of dunes under turbidity currents is suppressed by the presence of suspended loads.