Abstract: In this paper the entire process of an elastic-perfectly plastic rectangular beam with one degree of indeterminacy subjected to a concentrated force at its center is stUdied, The process is divided illto four stages: an elanic state in the whole beam; an elastic-plastic state in a region of the beam; an elastic-plastic state in two regions of the beam, till to forming the mechanism of flow with a plastic hinge at the fixed end, The deflection of the beam axis is derived at the four stages, Equations for integral constants and the reaction at support are established, These equations are used to calculate the reactions at support, deflections, loads and momeds at the end of each stage.