This paper presents the derivation and the physical meaning of the general fourth‐order linear differential equation (with sectionally continuous derivatives) of the deflection curve and its general formulation and solution as a multipoint boundary value problem. An algorithm is presented in which shearing forces, bending moments, deflections, critical load and natural frequency are calculated for (non‐)uniform beams and columns, with arbitrary lateral and axial, (dis)continuous distributed load functions and concentrated loads, on (intermediate) (elastic) supports.