Abstract: The joints of structure can be regarded as ideal and non-ideal. In this paper, a basic concept of a type of non ideal constraints at end of beam—an elastic joint is established. The slope-deflection equation is deduced and used for both the beam with two non-ideal ends and the beam with one non-ideal end and one ideal end. By comparison, the slope deflection equation with non-ideal constraint is more general and the old equations with ideal constraints is a special example of this new equation. The application of these equations and internal force variation of the structure with different constraints are explained in an given example.