AbstractA direct method is presented for the generation of shape functions for rectangular finite elements, with any desired continuity of the shape functions across the interelement boundaries, i.e., the shape functions can be of any prescribed class C^N, N = 0, 1, 2, 3 …. The method is illustrated with seven examples, four of which are previously published elements. The other three examples represent new elements, two of which are conforming C¹ elements, and the third one is of class C². One of the C1 elements and the C² element reproduce exactly all the terms up to the sextic polynomial.