Abstract: A mathematical model of damped flexural–torsional vibrations of monoclinic composite strip of constant-length rectangular cross section is proposed. The model is based on the refined Timoshenko beam-bending theory, the theory of generalized Voigt–Lekhnitskii torsion, and the elastic–viscoelastic correspondence principle in the linear theory of viscoelasticity. A two-stage method for solving a coupled system of differential equations is developed. First, using the Laplace transform in spatial variable, real natural frequencies and natural forms are found. To determine the complex natural frequencies of the strip, the found real values are used as their initial values of natural frequencies, and then the complex frequencies are calculated by the method of third-order iterations. An assessment is given of the reliability of the mathematical model and method of numerical solution performed by comparing calculated and experimental values of natural frequencies and loss factors. The results of a numerical study of the effect of angles of orientation of reinforcing fibers and lengths by the values of natural frequencies and loss factors for free–free and cantilever monoclinic stripes are discussed. It is shown that, for the free–free strip, the region of mutual transformation eigenmodes of coupled vibration modes arise for quasi-bending and -twisting vibrations of either even or odd tones. In the cantilever strip of the region of mutual transformation of eigenforms of coupled modes, vibrations occur for both even and odd tones.