This study was motivated by airframe noise in aircraft and blade-vortex interaction (BVI) noise in helicopters.  In this thesis, the sound generated by vortical disturbances in a subsonic flow around solid surfaces, using different vortex velocity formulations, was investigated by numerically solving the linearized or non-linearized Euler equations. Analytical solutions for this general case are not available because the wavelength of the generated acoustic wave is comparable to the vortex size, which is at variance to the compact source assumption of the acoustic analogy. Numerical errors associated with the discretization and boundary conditions were kept small using a high-order scheme with accurate non-reflecting boundary conditions.  Stagnation flow on a flat plate, flow around a stationary and rotating cylinder, and that about two cylinders were taken as prototypes of real-world flows with strong gradients of mean pressure and velocity. Single and periodic vortices were taken into consideration. In addition, the effect of vortex core size, the street distance, street frequency, and the Mach number of the mean flow on sound generation and propagation were examined.  The sound wave strength was found to be proportional to the vortex strength. If the acoustic pressure is normalized by the vortex strength, then all the distinct acoustic pressure profiles will collapse into single curve. Sound generation by vortex interaction with a solid surface, as well as its propagation, were found to be totally different between the Taylor's and Vatistas's vortices. The vortex core size and vortex street distance have minor influences on the acoustic pressure profile for sound waves radiated by the Vatistas vortex. Nevertheless, the change of the core size or the distance between the vortex rows significantly affects the sound pressure profile and sound directivity radiated by a Taylor vortex.  The effects of the non-linear terms on sound wave properties were also investigated. The non-linear influence was found to increase with the vortex strength. A lifting cylinder is shown not only to increase the sound wave amplitude, but also to shift its directivity.  The developed methods and computer codes can be used in the future as platforms to more elaborate methods that will predict the noise generated by multi-element airfoils, and the undercarriage of an aircraft. This will help reduce the need of costly, time consuming, wind tunnel and field experiments.