A relaxed similarity theory which can be applied to river madels with movable beds is established by modifying existing theory by Einstein and Chien(1954). Experimental data collected from river models with movable beds were used to evaluate the applicability of the proposed theory. Effects of similarity of flow. $Delta$F$Delta$M, and similarity of sediment movement, $Delta$$F_s$, were examined by analyzing the behavior of total river-bed change. The results show that the smaller $Delta$F$Delta$M or $Delta$$F_s$ is, respectively, the larger total sedimentation is. The modified similarity theory established in this study would be useful and practical whenever it is impossible or very difficult to satisfy strict theoretical requirments concerning the river model experiments with movable beds.