Abstract Müller-Breslau's theorem is formulated and proved for certain linear structures in forced stationary harmonic vibration. The theorem provides the structural analyst with a computationally attractive method for finding, in one and the same calculation, all coefficients (generally complex-valued) describing the influence on a reactive or sectional force in a fixed position by an external harmonic unit load acting in any position. Critical and dimensioning combinations of loads can thereby easily be found. Three numerical examples demonstrate applications to systems that are discrete and continuous, undamped and damped, and finite and infinite. It is shown how a standard computer program for the analysis of beam and frame vibration can be employed to calculate and plot harmonic influence lines by use of the Müller-Breslau technique. Physical experiments based on the same technique are discussed.