Abstract: The elastic buckling of compression bar under combined action of axial force and axial distributed load is studied by progressive integration method. The calculation formulas of critical force under axial concentrated force and axial distributed force under various boundary conditions are derived. The fourth-order differential equation of the compression bar under axial concentrated force and axial distributed load is established, and the fourth-order differential equation of the beam under uniformly distributed load is compared with the compression bar to obtain the initial function of the buckling function of the compression bar. The deflection function is substituted into the fourth-order differential equation of the compression bar as uniformly distributed external load for integration to obtain the next iterative deflection function. The critical force is obtained by using the criterion that the maximum deflection of the buckling mode function of two adjacent iterations is equal. Compared with the Euler critical force formula and the exact solution of Bessel function under the action of concentrated force and distributed force alone, satisfactory engineering precision can be achieved by two or three iterations. Under the combined action of axial force and distributed load, the concise expression of critical force can be obtained after three iterations, which can provide important guidance for the design of compression bar in practical engineering.