Abstract: The present paper focuses on the bending problem of heterogeneous beams with variable cross-section. Introducing piecewise linear functions to the inverse of the bending stiffness, the authors derived an analytic solution of the beam's deflection by using the Heaviside functions. The four parameters in the solution are determined by the support conditions. The method, which is known as the broken line converting method, has better accuracy and convergence than the step converting method. It is efficient for the calculation and optimal design of arbitrary heterogeneous structures and members with variable cross-section. An example is given to demonstrate the method.