Abstract <p>A problem on a conditional extremum that allows one to determine, based on the second limiting state, the upper limit of the maximum angular velocity of rotation of an axisymmetrically curved, fiber-reinforced disk is formulated. The structure is rigidly fixed to the vase or hub; blades can be attached to the outer edge of the disc blade. The materials of the components of the composition are assumed to be rigid-plastic, having asymmetry under tension and compression; the material of the binding matrix may have cylindrical anisotropy. Plastic deformation of the components of the composition is associated with piecewise linear yield criteria. The reinforcement structures of the disc web have meridional symmetry. A two-layer model of a curved disk with a plane-stress state in each of the fictitious composite layers is used. The discretized problem is solved using the simplex method of linear programming theory. The developed numerical algorithm has been verified. Examples of numerical calculation of the maximum angular velocity of rotation of flat, conical and spherical homogeneous and composite disks with different degrees of their curvature are analyzed. The cases of reinforcement of the disk web along geodetic directions and logarithmic spirals, as well as along meridional and circular trajectories, have been investigated. The comparison for disks of the same mass with the same consumption of reinforcement has been carried out. It has been shown that composite disks with a meridional-circumferential reinforcement structure have the highest load-bearing capacity. It has been demonstrated that even a slight axisymmetric curvature of the disk web leads to a sharp decrease in its load-bearing capacity compared to a similar flat structure.</p>