Long cylinder, subjected to internal pressure, is important in the analysis and design of nuclear fuel rod structures. In many cases, long cylinder problems have been considered as a plane strain condition. However, strictly speaking, long cylinder problems are not plane strain problems, but rather a general plane strain (GPS) condition, which is a combination of a plane strain state and a uniform strain state. The magnitude of the uniform axial strain is required, in order to make the summation of the axial force zero. Although there has been the GPS element, this paper proposes a general technique to solve long cylinder problems, using several pseudo-general plane strain (PGPS) elements. The conventional GPS elements and PGPS elements employed are as follows: axisymmetric GPS element (GA3), axisymmetric PGPS element (PGA8/6), 2-D GPS element (GIO), 3-D PGPS element (PG20/16), and reduced PGPS elements (RPGA6, RPG20/16). In particular, PGPS elements (PGA8/6, PG20/16) can be applied in periodic structure problems. These finite elements are tested, using several kinds of examples, thereby confirming the validity of the proposed finite element models.