This paper presents a numerical method for simulating the melting process in a cavity in the presence of wall vibration. An enthalpy method is employed to solve the governing equations associated with melting of an unfixed solid Phase Change Material (PCM) in a low gravitational environment. In this method, the problem is solved in one domain. The PCM, initially at its melting temperature, is placed inside a rectangular enclosure. The enclosure walls are then exposed to a uniform temperature under a specified amplitude and frequency of vibration. Melting begins from all sides, and due to natural convection, the PCM would not retain its initial shape. The governing equations are discretized by using a control-volume based finite difference method and are solved in together with solid PCM’s equation of motion. The results are presented in the form of a parametric study of the effects of aspect ratio, Stefan number, Strouhal number and dimensionless frequency or period of vibration, on the melt thickness, the solid PCM velocity and the volume of solid PCM. The melt thickness and solid PCM velocity are found to vibrate at the same frequency as of the exciting vibration. The melting rate increases with increase in Strouhal number while decreases with increase in dimensionless frequency of vibration. As seen from the results, for very high frequencies of vibration the melt thickness and molten volume fraction essentially approach those for without vibration. The results show that for the range of parameters investigated, vibration can enhance the melting rate up to 15%.