The performance of triangular elements satisfying either compatibility or incompatibility conditions in the plate bending analyses is of great importance. To achieve highly accurate responses, four elements are formulated for the structural analysis in this study. All of these elements have thirteen nodes with different degree-of-freedom arrangements. Two of them are displacement-based compatible triangular elements, which are named Karimi Pour Compatible Triangular (KCT) and Noroozinejad Compatible Triangular (NCT) elements. Besides, the other two stress-based incompatible triangular elements are also suggested with the names of Karimi Pour Incompatible Triangular (KIT) and Noroozinejad Incompatible Triangular (NIT) elements. In this study, several benchmark problems are solved by using four proposed elements. These structures were previously analyzed by analytical or numerical schemes. Findings clearly indicated the improvement of answers, when various behaviors of the plate bending structures were studied. Additionally, it is concluded that the solution time is considerably declined if the recommended stress-based elements are utilized.