This paper aims to propose a generalized finite element technique that can accurately approximate the solution of the flexural-shear cantilever model of wall-frame structures proposed by Heidebrecht and Stafford Smith. This approach adopts scaled monomials as enrichment functions, and they are highly effective in accurately capturing the solution of the problem, as it consists of smooth functions such as polynomials, hyperbolic and trigonometric functions. Several numerical experiments are performed on the static and modal analyses of the flexural-shear cantilever wall-frame structures using the proposed generalized finite element method (GFEM), and their accuracies are compared with those obtained using the standard finite element method. The proposed GFEM is able to achieve theoretical convergence rates of the static and modal analyses, which are, in principle, identical to those of the standard FEM, for various polynomial orders of its shape functions such as quadratic, cubic and quartic orders. The proposed GFEM with quartic enrichment functions can provide more accurate solutions than the standard FEM, and thus can be effectively used at the initial design stage of high-rise wall-frame structures. This work is the first paper where the GFEM is applied to the analysis of high-rise wall-frame structures, and the developed technique can be used as a good analysis tool at the initial design stage.