This paper is a survey of the use of assumed stress hybrid finite element methods for analyzing plate and shell structures. It describes the construction of Kirchhoff plate element by complementary energy principle, and of Reissner-Mindlin plate element by Hellinger-Reissner principle. Special hybrid stress elements are used to model joining of elements which are not coplanar. Such elements include the so-called semiLoof plate elements and 3D-solid elements tailored for analyzing thin plates and shells.
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