The hybrid-Trefftz finite element method (HT-FEM) is an efficient numerical tool in computational mechanics for solving complex boundary value problems [1-3]. This method uses two independent displacement fields to describe the internal domain and element boundary. Such internal displacement fields are chosen as a priori satisfying the governing differential equations. By variational principle, the minimization of total potential energy leads to an integration along the element boundary only. As a result, HT-FEM possesses the advantages that a large element with arbitrary polygonal or curve sides can be generated, which looks like the one generated by boundary element. In contrast to boundary element, the HT-FEM does not require the fundamental solutions which may not be easy to obtain. Instead, a relatively easy and systematic way has been introduced to get the Trefftz complete set of homogeneous solutions (generally called T-complete set) satisfying the governing differential equations. For elasticity problems, most of them are from the Muskhelishvili’s and Lekhnitskii’s complex variable formulation for isotropic and anisotropic elastic materials, respectively [4,5]. Due to the above-mentioned advantages, several extensional works have been done by HT-FEM. However, due to the complexity, this method is yet not extended to the coupling analysis of in-plane and anti-plane anisotropic elastic problems. If an arbitrarily laminated composite plate is considered, the coupling of in-plane and anti-plane deformations cannot be avoided. To generate the T-complete set for the two-dimensional coupling analysis, we utilize the well-known complex variable Stroh formalism [6]. Due to the simplicity and generality of the matrix form solution provided by Stroh formalism, the final system of equations can be constructed in a systematic way and be called Stroh-Trefftz finite element method (ST-FEM). Moreover, due to the unified feature of Stroh formalism, ST-FEM will then be easily extended to the problems with viscoelastic, piezoelectric, piezomagnetic, and magnetic-electro-elastic materials.