A long cylinder composed of periodic structures along the axis can not be treated as a general plane strain(GPS) state, because within a repeated module, the geometry and loading condition may not be uniform along the axial direction. For this kind of situation, a ‘ more general kind of GPS ’ finite element is needed that uses a set of ‘ planar constraints ’, hereinafter called a ‘ pseudo general plane strain(PGPS) finite element ’. Otherwise, a high number of constraints need to be used, which is a tedious job and often gives rise to an input error. Plus, this can also cause a numerically ill conditioned stiffness matrix that results in a trivial or diverged solution. Accordingly, this study proposes several PGPS finite elements that use a set of planar constraints to solve long periodic cylinder problems, as well as conventional long cylinder and plane strain problems.