A numerical method for the analysis of normally loaded articulated beams on elastic supports is presented. The method is an iteration procedure using numerical integration to solve the differential equations governing the action of the beams. The procedure is applied to beams made up of straight line segments. Cross sections are allowed to vary. Two alternate methods are discussed. One uses the numerical integration technique to calculate deflections in terms of an assumed moment, shear, slope, twist or deflection. The true deflection can be determined by considering boundary conditions of the beam. The second alternate method uses the numerical integration technique to find influence coefficients, which are used in a general method solution. The alternate methods are not iteration procedures. Examples which apply these methods to various support conditions are given. Advantages of each method are given. Convergence of the iteration procedure is discussed.