The analytical trial functions methods (ATFM) have been studied systematically in this paper. In the view of the weighted residual methods, the selection of the trial functions is very important to the effectivity of the computational methods. The analytical trial functions methods choose the analytical solutions of the problem as the trial functions of the unknown fields, such as the displacement or the stress in the elastic mechanics problems. However, due to the consistent of the trial functions in the analysis region, when the boundary condition is dealt with in the right way, the computation will be very fine. The generalized conforming methods and the hybrid elements methods are employed to formulate the elements based on the analytical trial functions. It is very successful in this new kind of finite element methods, and series plane elements are presented in this paper. More attractively, the elements can perform very well even in the seriously distorted meshes, which is still a challenge to some other finite element methods. The present ATFM possesses the advantages of both analytical and discrete method; its potential will be shown with the continued study.