We present to obtain the equations of motion of the axially composite beams. The composite beams are produced from two or more different materials. In this study, the material varies along the beam axis. In other words, it is seen that the beam is made of different materials, as the beam proceeds along its axis. The material is homogeneous and the beam is formed by combining the step by step along the beam axis. The mathematical model of this problem can be presented in two different ways. In the first, a multispan beam approach is used. In this approach, the variation of each material is given as one span. The equation of motion is obtained as number of various material and four different transient conditions are written for each material alteration point. In the other, one equation is introduced. This equation contains the discontinuity function. The material variation is modeled with the discontinuity functions. Thus, two different models are obtained for only problem.