Airy beams have become an important beam shape for structured light beams because of their interesting self-accelerating and parabolic propagation properties. Many variants of Airy beams have been proposed, among which the Airy beam with cylindrical symmetry [also known as the circular Airy beam or abrupt autofocusing (AAF) beam] is particularly peculiar and has attracted special attention due to its shape transformation during propagation. Much effort has been devoted to understanding the properties of the AAF beam. In this work, we present simulation results for generating the AAF beam using a phase-only mask. A cubic chirp-modulated axicon phase is used to create the mask. We found an optimal value for the axiconic phase, and the cubic phase is essential for controlling the AAF beam's shape. We demonstrate that a phase-only mask is an effective and simple method for generating high contrast between the initial and AAF plane. We present the results for beam formation and propagation dynamics of the AAF beam using the control parameters of the phase mask. We also discuss the design parameters and their influence on the AAF beam shapes. Our results pave the way for a deeper understanding of the beam formation and propagation dynamics of the AAF beam.