The model of generalized thermoelasticity proposed by dual phase lag (DPL), is applied to study the thermoelastic interactions in an infinite fiber-reinforced anisotropic medium with a circular hole. A decaying with time thermal field on the boundary of the hole, which is stress free, causes the thermoelastic interactions. The solutions for displacement, temperature, and stresses are obtained with the help of the finite element procedure. The effects of the reinforcement on temperature, stress, and displacement are studied. The exact solution in the case of isotropic medium is discussed explicitly. The accuracy of the finite element method validated by comparing between the finite element and exact solutions for absence the reinforcement.