AbstractPenalty methods have been proposed as a viable method for enforcing interelement continuity constraints on nonconforming elements. Particularly for fourth‐order problems in whichC1‐continuity leads to elements of high degree or complex composite elements, the use of penalty methods to enforce theC1‐continuity constraint appears promising. In this study we demonstrate equivalence of the finite‐element penalty method to a hybrid method and provide a stability analysis which implies that the penalty method is stable only if reduced integration of a certain order is used. Numerical experiments confirm that the penalty method fails if this condition is