This article examines new cylindrically anisotropic materials, including winding composite materials reinforced with various fiber, and a mathematical solution of the fourth-order partial differential equation with two variables in polar coordinates.Purpose: Ther aim of this work is to study anisotropy properties of composite materials with cylindrical anisotropy.Methodology/approach: Foe a solution, equations are translated into Cartesian coordinates, and stress functions are used as a sum of polynomials. As a result of the solution, two relations are obtained between the elastic constants in the main direction of anisotropy, i.e., elasticity parameters. These parameters are important to determine the mechanical properties of anisotropic material.Research findings: New high-strength composite materials are improved to apply in new technologies for building design and construction, high-strength structures are obtained using synthetic composite materials.Originality/value: Elastic constants for cylindrically anisotropic materials represent an innovative approach to determine the properties of composite materials with a flat anisotropy scheme, which make it easier and more efficient to determine elasticity parameters and strength in an arbitrary direction of coordinate axes.