In this work, a vibroacoustic model is developed to predict the dynamic response and sound radiation of an axisymmetric railway wheel under a non-axisymmetric excitation. To do this, first, the energy equation of the wheel is analytically integrated along the circumferential direction after an expansion of its response as Fourier series. Then, the vibrational dynamics of the three-dimensional wheel is solved through a set of two-dimensional problems which come from that integration. Subsequently, the three-dimensional sound radiation of the railway wheel is calculated from the solution of the aforementioned two-dimensional problems by means of analytical relations based on the harmonic distribution of the dynamics in the circumferential coordinate. Additionally, the wheel rotation is introduced in the model using an eulerian approach, in order to consider the associated gyroscopic and inertial effects. The proposed model presents a greater computational efficiency compared to full three-dimensional methodologies, without compromising the precision of the results. This allows the implementation of the sound radiation calculation in optimization algorithms with the aim of achieving quieter designs of railway wheels.