A model based on the relations of a hereditarily elastic medium, an anisotropic theory of elasticity, and the Volterra correspondence principle has been developed, which allows one to calculate and predict the anisotropy of the rheological properties of unidirectional carbon fiber in a linear area. Based on the proposed model, expressions are obtained for the stress strain curves of unidirectional samples, which were tested on samples made of carbon fiber reinforced plastic IM7/8552 and carbon fiber plastic AS4/3501-6, loaded at different angles to the direction of reinforcement and strain rates corresponding to quasistatic and dynamic loading. It was assumed that the time dependent properties of unidirectional carbon fiber reinforced plastics are manifested in the direction perpendicular to the reinforcement and in-plane shear of the layer. The implementation of the calculation algorithm turned out to be possible due to the use of relations of the algebra of the resolvent operators. To obtain numerical values of the model parameters, the experimental curves of the deformation of carbon fiber samples were processed.