Linear stability analysis is applied to the cylinder‐plate and wedge‐plate problems. Necessary conditions for the solution to exist are obtained. These conditions give bounds on the number of ribbing lines at given capillary number and spacing. The results are compared with previous numerical work for the cylinder‐plate problem. It is shown that a simple theory accurately predicts the distance at which the meniscus is formed for the wedge and plate problem. The technique can be generalized to other coating processes such as roll coating.