When estimating a structure's fatigue life during vibrational test the stress frequency-response function (SFRF) to the base excitation is required. The response to this base excitation can be numerically obtained by solving the equilibrium equations for each frequency of interest. In this research we propose a new method, that can be used to obtain the SFRF of a base-excited structure using the modal model of the unconstrained structure, only. By further developing the idea of a structural modification using the response function this research significantly reduces the computation time and the amount of data sent to the fatigue-analysis software. The new method is presented on two numerical examples: a simple beam structure and a Y-shaped structure. Using numerical examples, the effects of the modal truncation, the matrix singularity and the damping are discussed.