Abstract: One-dimensional (1D) components as rod, shaft and beam are widely used in engineering structures. This paper investigates the nodal displacement accuracy of 1D high-order rod element and beam elements subjected to arbitrary polynomial distributed loads. First, the exact solutions are derived for the uniform fixed-free rod and the Euler beam as well as the Timoshenko beam,then the free-end nodal displacements are obtained by using a second-order rod element, a fifth-order Euler beam element and a third-order Timoshenko beam element, respectively. By comparing the FEM results with the exact solutions, it is shown that accurate nodal displacements can be obtained by using linear or high-order rod elements, and cubic or high-order Euler and Timoshenko beam elements. Moreover, by taking the second-order rod element as an example, the present results and conclusions are validated by using the static condensation method.