The effects of the blockage of a rectangular intake duct and impervious flow boundaries on the critical submergence of a rectangular intake are presented. The potential solution, based on the Rankine stagnation point, is determined to be another approximate method for the prediction of the critical submergence of this kind of intake. It is found that a critical cylindrical sink surface capped with two critical hemispherical sink surfaces at both ends with a radius equal to the radial distance of the stagnation point (which is 2/pi times the critical submergence of the rectangular intake) can also be used to predict critical submergence. Theoretical results and available experimental data are compared. The theory presented in this study acceptably (by about 1-20%) estimates the critical submergence for the cases where the distance (clearances) of the impervious solid boundaries are larger than 1/2 of the small inner dimension of the intake. On the other hand, the theory overestimates the critical submergence by about 80% for the cases where the distances of the solid boundaries (especially those cutting the free surface such as the dead-end wall) become zero.