A process for producing an acoustic device having a phononic crystal structure comprising inclusions produced in a first medium distributed in a matrix of a second medium, to block propagation of acoustic waves within a bandgap frequency band, includes: defining geometric parameters of said inclusions, which have walls contacting said matrix, making at least one non-zero first wall angle, to the normal of the plane of said structure, said geometric parameters including said first wall angle; determining a function relating to variation in frequency position of said bandgap with said wall angle or relating to variation in width of said bandgap with said wall angle; determining said at least first angle, for a selected frequency position and/or selected width of the bandgap, from the function or functions determined beforehand; and producing said inclusions having at least said first wall angle in said matrix formed by said second medium.