Critical flows may occur at more than one depth in channels having compound cross-sections (cross-sections with flood plains). The possibility of multiple critical depths affects the water-surface-profile calculations. Presently available algorithms determine only one of the critical depths which may lead to large errors. In this paper, computational procedures are presented for computing all the possible critical depths in general symmetrical, compound channels. They incorporate a general definition of Froude number based on the one-dimensional unsteady momentum and continuity equations. In these procedures, the total number of critical depths possible in a cross-section for a given discharge are first determined and then their values are computed one by one in an efficient manner. A procedure is presented to design a compound channel section so that there is only one critical depth, thereby reducing the range of flow depth over which flow may be highly unstable. Two typical examples are presented to illustrate the effect of multiple critical depths on the water-surface profile computations.