The invention relates to a method for manufacturing an aircraft turbine engine housing, the housing (23) comprising: an annular shell (29) with axis A; —an annular element (24; 253, 254) attached to the inside of the shell (29), the annular element comprising a body (25) made of NIDA-type cellular material and comprising a downstream portion (252) covered with an abradable material (26), and an upstream portion (251) without abradable material, the body (25) extending in a continuous manner from the upstream portion (251) to the downstream portion (252), the method comprising: —manufacturing the annular element in the form of a continuous annular body, —cutting the annular body into segments (253, 254), —attaching the segments to the shell, and —depositing the abradable material (26) onto the inside surface (25a) of the downstream portion (252).