A method for producing an austenitic alloy pipe, comprising: a process for producing an austenitic alloy material pipe consisting of, by mass percent, C: at most 0.03%, Si: 0.10 to 1.0%, Mn: 0.3 to 5.0%, Ni: 23 to 52%, Cr: 20 to 30%, N: 0.005 to 0.50%, Mo: 1.5 to 9%, and Cu: 0.5 to 3%, and optionally at least one type selected from a group consisting, by mass percent, of Ca: at most 0.01%, Mg: at most 0.01%, and REM (rare earth metal): at most 0.20%, the balance being Fe and impurities; a process for cold-working the material pipe; and a process for producing an austenitic alloy pipe, wherein by subjecting the cold-worked material pipe to straightening with a maximum crush ratio of 2.0 to 15.0% and low-temperature heat treatment at 300 to 550°C for at least 5 minutes, the alloy pipe is provided with a tensile yield strength YS LT of at least 689.1 MPa in a pipe axial direction of the alloy pipe, and wherein for the alloy pipe, the tensile yield strength YS LT, a compressive yield strength YS LC (MPa) in the pipe axial direction, a tensile yield strength YS CT (MPa) in the pipe circumferential direction, and a compressive yield strength YScc (MPa) in the pipe circumferential direction satisfy Formulas to, 0.90 ≤ YS LC / YS LT ≤ 1.11 0.90 ≤ YS CC / YS CT ≤ 1.11 0.90 ≤ YS CC / YS LT ≤ 1.11 0.90 ≤ YS CT / YS LT ≤ 1.11 wherein the process for producing the austenitic alloy material pipe comprises hot-working, and the material pipe is produced from a round billet (i) by an extrusion pipe production method represented by the Ugine-Sejournet process, or (ii) by the Mannesmann pipe making process, the process for cold-working the material pipe is either cold drawing or cold rolling, and the reduction of area at the time of cold working is 15.0% or more. a process for producing an austenitic alloy material pipe consisting of, by mass percent, C: at most 0.03%, Si: 0.10 to 1.0%, Mn: 0.3 to 5.0%, Ni: 23 to 52%, Cr: 20 to 30%, N: 0.005 to 0.50%, Mo: 1.5 to 9%, and Cu: 0.5 to 3%, and optionally at least one type selected from a group consisting, by mass percent, of Ca: at most 0.01%, Mg: at most 0.01%, and REM (rare earth metal): at most 0.20%, the balance being Fe and impurities; a process for cold-working the material pipe; and a process for producing an austenitic alloy pipe, wherein by subjecting the cold-worked material pipe to straightening with a maximum crush ratio of 2.0 to 15.0% and low-temperature heat treatment at 300 to 550°C for at least 5 minutes, the alloy pipe is provided with a tensile yield strength YS LT of at least 689.1 MPa in a pipe axial direction of the alloy pipe, and wherein for the alloy pipe, the tensile yield strength YS LT, a compressive yield strength YS LC (MPa) in the pipe axial direction, a tensile yield strength YS CT (MPa) in the pipe circumferential direction, and a compressive yield strength YScc (MPa) in the pipe circumferential direction satisfy Formulas to, 0.90 ≤ YS LC / YS LT ≤ 1.11 0.90 ≤ YS CC / YS CT ≤ 1.11 0.90 ≤ YS CC / YS LT ≤ 1.11 0.90 ≤ YS CT / YS LT ≤ 1.11 wherein the process for producing the austenitic alloy material pipe comprises hot-working, and the material pipe is produced from a round billet (i) by an extrusion pipe production method represented by the Ugine-Sejournet process, or (ii) by the Mannesmann pipe making process, the process for cold-working the material pipe is either cold drawing or cold rolling, and the reduction of area at the time of cold working is 15.0% or more.