A pipe support structure for supporting a pipe (12, 13) supported at a first clamp position (L1, L2) and a second clamp position (L1, L2), the pipe having a fluid passage formed therein to allow a fluid at a high temperature to pass therethrough, and made of a resilient material, comprises: a retaining member for resiliently retaining the outer peripheral portion at at least one of the first clamp position and the second clamp position, the pipe having an inclined portion (12d, 13d) inclined with respect to a horizontal plane perpendicular to the gravity direction, and a bent portion (12a, 13a) having a predetermined radius of curvature, the inclined portion and the bent portion being disposed between the first clamp position and the second clamp position, the retaining member having a predetermined spring constant and a predetermined attenuation coefficient, the pipe being subjected to a Coriolis force and having a heat expansion amount caused by the Coriolis force when the fluid passage allows the fluid at the high temperature, the retaining member having a reaction force acting against the Coriolis force, at least one of the first clamp position and the second clamp position and the shape of the bent portion being set, and the spring constant and the attenuation coefficient of the retaining member being set in such a manner that the reaction force of the retaining member generated in response to the Coriolis force generated on the pipe acts to suppress the heat expansion amount caused by the Coriolis force from being increased when the fluid passage allows the fluid at the high temperature, and characterized by, when the Coriolis force is represented by F c, the fluid angular speed of the fluid passing through the fluid passage is represented by ω, and the time is represented by t, the Coriolis coercive force f c temporally varying in response to the vibration of the pipe is given by f c (t) = F c sin ωt, when the reaction force caused on the retaining member against the Coriolis force F c is represented by F r, and the clamp reaction force caused on the retaining member and temporally varying in response to the Coriolis coercive force f c (t) is represented by f r (t), the clamp reaction force f r (t) is given by f r (t) = Fr sin (ωt - φ), where φ is a phase difference, when the coefficient to be determined in response to the ratio of the clamp reaction force f r (t) with respect to the Coriolis coercive force f c (t) is "k", the first clamp position, the second clamp position, the shape of the bent portion, the spring constant, and the attenuation coefficient being set to have the coefficient "k" in the following equation approximately 1. f c t = - κ f r t a retaining member for resiliently retaining the outer peripheral portion at at least one of the first clamp position and the second clamp position, the pipe having an inclined portion (12d, 13d) inclined with respect to a horizontal plane perpendicular to the gravity direction, and a bent portion (12a, 13a) having a predetermined radius of curvature, the inclined portion and the bent portion being disposed between the first clamp position and the second clamp position, the retaining member having a predetermined spring constant and a predetermined attenuation coefficient, the pipe being subjected to a Coriolis force and having a heat expansion amount caused by the Coriolis force when the fluid passage allows the fluid at the high temperature, the retaining member having a reaction force acting against the Coriolis force, at least one of the first clamp position and the second clamp position and the shape of the bent portion being set, and the spring constant and the attenuation coefficient of the retaining member being set in such a manner that the reaction force of the retaining member generated in response to the Coriolis force generated on the pipe acts to suppress the heat expansion amount caused by the Coriolis force from being increased when the fluid passage allows the fluid at the high temperature, and characterized by, when the Coriolis force is represented by F c, the fluid angular speed of the fluid passing through the fluid passage is represented by ω, and the time is represented by t, the Coriolis coercive force f c temporally varying in response to the vibration of the pipe is given by f c (t) = F c sin ωt, when the reaction force caused on the retaining member against the Coriolis force F c is represented by F r, and the clamp reaction force caused on the retaining member and temporally varying in response to the Coriolis coercive force f c (t) is represented by f r (t), the clamp reaction force f r (t) is given by f r (t) = Fr sin (ωt - φ), where φ is a phase difference, when the coefficient to be determined in response to the ratio of the clamp reaction force f r (t) with respect to the Coriolis coercive force f c (t) is "k", the first clamp position, the second clamp position, the shape of the bent portion, the spring constant, and the attenuation coefficient being set to have the coefficient "k" in the following equation approximately 1. f c t = - κ f r t