In this paper, we propose a semi-analytical framework, the scaled boundary finite element method (SBFEM) to study acoustic problems in the mid-frequency range. The SBFEM shares the advantages of both the finite element method (FEM) and the boundary element method (BEM). Like the FEM, it does not require the fundamental solution and similar to the BEM only the boundary is discretized, thus reducing the spatial dimensionality by one. The solution within the domain is represented analytically whilst on the boundary it is represented by finite elements. Different choices of boundary representations are possible, however, here we explore only Lagrangian description. The proposed framework is verified against closed-form solutions and direct comparisons are made with conventional FEM based on Lagrangian descriptions; this will be demonstrated using a two-dimensional car cavity model available from the literature. The improved accuracy and reduced computational time can be attributed to the semi-analytical formulation combined with the boundary discretization. © 2017 Institute of Noise Control Engineering. All rights reserved.