Method for optimising a low-cycle, and optionally high-cycle, fatigue test rig (100, 200), said test rig being intended to reproduce a support of turbine engine parts, and comprising a support member which is fixed to a mount and defines at least two bearing surfaces, and a test piece which is connected to traction means for loading the test piece so that it bears against the or each bearing surface of the support member, the method comprising the steps consisting in: - determining variable parameters of the support member and/or the test piece, as well as ranges of variation of said variable parameters, - determining at least one objective to be achieved or optimised, a variation of the values of at least some of the above-mentioned variable parameters affecting the objective, - modifying one or more of the values of the above-mentioned variable parameters, in the respective ranges thereof, and determining those which make it possible to achieve or optimise the objective so as to identify optimised parameters, and - producing a support member and/or a test piece based on fixed parameters and parameters optimised for equipping a new test rig, or modifying the support member and/or the test piece of an existing test rig based on the optimised parameters, and characterised in that, the support member extends along a longitudinal direction and further comprising two middle portions respectively supporting the two bearing surfaces, each middle portion being connected, on the side opposite the traction means, by a first arm to a base for fixing to the mount and, each of the middle portions being connected, on the side of the traction means, by a pair of second arms to first ends of two parallel crossbars which are at a distance from one another, second opposite ends of the bars being connected by another pair of second arms to the other middle portion, on the side of the traction means, the two pairs of second arms and first arms extending along the longitudinal direction and in opposite direction with regard to the middle portions, and, the method includes among the variable parameters at least one dimension of the second arms of each pair, and/or the angle of inclination of said second arms with respect to the corresponding crossbar or with respect to the bearing surface of the corresponding middle portion, the objective to be achieved is selected from the group comprising the parallelism and the contact of the bearing surfaces (124, 148) between the test piece and the support member, a maximum amplitude of sliding between said bearing surfaces, and a homogeneous contact pressure between said bearing surfaces, and a combination of the ones. - determining variable parameters of the support member and/or the test piece, as well as ranges of variation of said variable parameters, - determining at least one objective to be achieved or optimised, a variation of the values of at least some of the above-mentioned variable parameters affecting the objective, - modifying one or more of the values of the above-mentioned variable parameters, in the respective ranges thereof, and determining those which make it possible to achieve or optimise the objective so as to identify optimised parameters, and - producing a support member and/or a test piece based on fixed parameters and parameters optimised for equipping a new test rig, or modifying the support member and/or the test piece of an existing test rig based on the optimised parameters, and the support member extends along a longitudinal direction and further comprising two middle portions respectively supporting the two bearing surfaces, each middle portion being connected, on the side opposite the traction means, by a first arm to a base for fixing to the mount and, each of the middle portions being connected, on the side of the traction means, by a pair of second arms to first ends of two parallel crossbars which are at a distance from one another, second opposite ends of the bars being connected by another pair of second arms to the other middle portion, on the side of the traction means, the two pairs of second arms and first arms extending along the longitudinal direction and in opposite direction with regard to the middle portions, and, the method includes among the variable parameters at least one dimension of the second arms of each pair, and/or the angle of inclination of said second arms with respect to the corresponding crossbar or with respect to the bearing surface of the corresponding middle portion, the objective to be achieved is selected from the group comprising the parallelism and the contact of the bearing surfaces (124, 148) between the test piece and the support member, a maximum amplitude of sliding between said bearing surfaces, and a homogeneous contact pressure between said bearing surfaces, and a combination of the ones.