This paper presents the frequency domain formulation of the Green's Functions Stiffness Method (GFSM) for plane Euler–Bernoulli frames subjected to arbitrary external loads (forces and bending moments). The GFSM is a generalization of the Stiffness Method (SM) or the Finite Element Method (FEM) that computes the closed-form analytical structural response by decomposing it into a homogeneous and a fixed or particular responses. The homogeneous response is obtained from the displacements at the element ends in the absence of external loads, while the fixed response is calculated using the Green's functions of fixed elements through a superposition integral that includes the external loads. The GFSM can be categorized as a mesh reduction method that generalizes the Spectral Element Method (SEM), in which the structural response is first obtained in the frequency domain and then converted to the time domain using the Fast Fourier Transform algorithm. Compared to the SEM, the significant advantage of the GFSM is that the frequency domain structural response is exact and avoids the need for dense meshes when external loads have complex patterns. Three examples are presented to demonstrate the effectiveness of the GFSM, each of which shows excellent agreement when compared to the FEM solution even using far fewer elements.