We present a DUNE module that provides three new types of finite elements, namely the cubic Hermite element on simplices, the quadratic Morley and the quintic Argyris triangle. They give DUNE the capability to formulate conforming methods for fourth order problems in one and two dimensions. We detail out, how they handle the lack of affine equivalence while still being usable on the
reference element, and discuss their positioning within the DUNE framework. Additionally, a particular focus lies on the possibility to strongly enforce essential boundary conditions. Including these elements in DUNE routines and higher level discretization modules solely requires an adaptation of the global interpolation routine in order to allow the evaluation of derivatives as degrees of freedom and a minor adaption in the treatment of boundary conditions. We verify that the implemented elements attain their theoretically predicted convergence rate for a series of numerical experiments, ranging from second order elliptic problems to the minimization of a von-Kármán energy.