A research paper A SBFEM (scaled boundary finite element method) based approach is developed for dealing with the third boundary condition of 2-D elastic systems, and the cyclic symmetry is exploited to reduce the computational expense. The basic SBFEM equations of solving the systems supported by linear spring are presented. On this basis, the equations of solving systems with other more kinds of boundary conditions (nonlinear spring support, viscoelastic spring support, internal spring link and inclined support) are derived. Furthermore, a proof that the eigenvalue matrix of SBFE equations is block-circulant is presented for the structure with cyclic symmetry, and both the eigenvalue and system equations of SBFEM are partitioned into a number of smaller independent problems which are solved by a partitioning algorithm. Numerical examples are given to illustrate the correctness and efficiency of the proposed approach.