The inscription of customized fiber Bragg structures under acoustic excitation is proposed and demonstrated. By setting the proper acoustic excitation function, the desired spectrum of the grating can be achieved. In this paper, the effect of applying a burst acoustic wave during the process of Bragg grating inscription using the direct writing method through a phase mask is investigated. Among all the characteristics that can be changed due to a periodic defect insertion in the uniform Bragg structure, the control of phase is used to demonstrate this assertion. The results of numerical simulations are shown to be in excellent agreement with experiments. It can be further extended to generate multiple phase shifts in optical fiber and/or waveguides, if the defects are inserted at different positions, as is shown.