In this paper, the problems involved in the process of degeneration of quadrilateral element into triangular element are thoroughly analysed. The contents include the formulation of the geometry mapping induced by collapsing one side of the quadrilateral element and the construction of the shape functions. The study focuses first on a 4-node bilinear quadrilateral (Q4) element to 3-node constant strain triangular (CST) element, and then on a 8-node serendipity (Q8) element to 6-node triangular element(T6). In the analysis, the quadrilateral element and degenerate triangular element are assumed to be enclosed by straight edges. The theoretical results show that there is another better approach to realize the degeneration, and that even for conventional approach of degeneration we can give more reasonable explanation to the unclear problems like the CST property in degenerate CST element and the necessity of the additional terms in degenerate T6 element. Copyright