Abstract: A new method for arbitrary elastic beam analysis is presented. A general expression for determining deflections and slopes of elastic beams is developed using a method combining singularity functions with Laplace transformations, and support reactions and deformation constants-deflection and slop of the left end are determined with boundary conditions and deformation conditions of the beams. This method can be used for statically determinate beams or statically indeterminate beams arbitrarily made up of different kinds of supports：hinged support, movable support, fixed support, elastic support and clearance support, borne different kinds of loads：concentrated force, concentrated moment and uniform load, and had arbitrary stepped shapes, can determine its supporting reactions and deflection and slope at any section easily and accurately. It has practical value in computer analysis, optimum design and CAD for complicated stepped beams.

Key words: Arbitrary beam, Bending deflection, General method, Support reaction