A gas turbine engine comprising a gas turbine casing forming a cylindrical member which extends in a substantially axial direction and in a circumferential direction, the axial direction being a direction parallel to an axial center which is a center of rotation of a first and second rotor shaft (27,28) of the gas turbine engine, and the circumferential direction being around the axial center, wherein the cylindrical member has a machined hole for attaching an external component and a stress reduction structure for preventing a circumferential tensile load with respect to the machined hole and reducing a stress concentration due to high thermal stress and hoop stress repeatedly applied at start and stop of the gas turbine engine, and wherein the stress reduction structure comprises a recess provided on a radial inner or outer side of the cylindrical member where the machined hole is open and formed on a circumferential side-portion of the machined hole the recess having a distance to an opening edge of the machined hole formed in the cylindrical member and being recessed in a depth direction of the machined hole, characterized in that the recess is formed by a columnar end mill having its rotary shaft (Ce) inclined such that a part of a leading edge of the end mill is in contact at an angle with a surface of the cylindrical member for defining a circular arc portion where a part of an opening edge is formed in a circular arc shape, an open portion where the circular arc shape is open and a part of the opening edge is formed by both ends of the open portion being linearly connected, and an inclined surface, wherein a bottom portion of the recess is formed so as to be gradually decreased in depth by the inclined surface from a central portion of the circular arc portion which is the deepest part of the recess along the circular arc portion toward the linear side of the open portion, and a side of the circular arc portion having a relatively deep bottom portion is disposed facing toward the machined hole, wherein the recess has a deepest depth (h) at the central portion of the circular arc portion within a range of 50% or less of a plate thickness of the cylindrical member in the radial direction in which the machined hole is formed, wherein the shortest distance between the opening edge of the recess and the opening edge of the machined hole is within a range of 50% or less of a circumferential diametral dimension of the machined hole, wherein a circumferential diametral dimension of the recess is within a range of 100% or more to 300% or less of the circumferential diametral dimension of the machined hole, and wherein an axial diametral dimension (w) of the recess is within a range of 100% or more to 300% or less of an axial diametral dimension of the machined hole and the axial diametral dimension of the machined hole is included in a circumferential position in the range of the axial diametral dimension (w) of the recess. wherein the cylindrical member has a machined hole for attaching an external component and a stress reduction structure for preventing a circumferential tensile load with respect to the machined hole and reducing a stress concentration due to high thermal stress and hoop stress repeatedly applied at start and stop of the gas turbine engine, and wherein the stress reduction structure comprises a recess provided on a radial inner or outer side of the cylindrical member where the machined hole is open and formed on a circumferential side-portion of the machined hole the recess having a distance to an opening edge of the machined hole formed in the cylindrical member and being recessed in a depth direction of the machined hole, characterized in that the recess is formed by a columnar end mill having its rotary shaft (Ce) inclined such that a part of a leading edge of the end mill is in contact at an angle with a surface of the cylindrical member for defining a circular arc portion where a part of an opening edge is formed in a circular arc shape, an open portion where the circular arc shape is open and a part of the opening edge is formed by both ends of the open portion being linearly connected, and an inclined surface, wherein a bottom portion of the recess is formed so as to be gradually decreased in depth by the inclined surface from a central portion of the circular arc portion which is the deepest part of the recess along the circular arc portion toward the linear side of the open portion, and a side of the circular arc portion having a relatively deep bottom portion is disposed facing toward the machined hole, wherein the recess has a deepest depth (h) at the central portion of the circular arc portion within a range of 50% or less of a plate thickness of the cylindrical member in the radial direction in which the machined hole is formed, wherein the shortest distance between the opening edge of the recess and the opening edge of the machined hole is within a range of 50% or less of a circumferential diametral dimension of the machined hole, wherein a circumferential diametral dimension of the recess is within a range of 100% or more to 300% or less of the circumferential diametral dimension of the machined hole, and wherein an axial diametral dimension (w) of the recess is within a range of 100% or more to 300% or less of an axial diametral dimension of the machined hole and the axial diametral dimension of the machined hole is included in a circumferential position in the range of the axial diametral dimension (w) of the recess.