The paper is devoted to finite element modelling of the beam vibration process, taking into account the complex internal structure of the material. In the finite element model of the beam external damping (air damping) and internal damping are taken into account. The external part of the damping forces is considered local, i.e. depending on the velocity of element nodes only at the current moment. Internal damping is considered nonlocal in time, i.e. depending on the velocities on the vibration time history. Unlike the nonlocal in space damping model nonlocal in time model can be easily integrated to the finite element analysis algorithm. The central differences method is used to solve the dynamic equilibrium equation and the continuous internal damping kernel function is replaced by its discrete equivalent. The beam vibration model considering nonlocal damping is implemented in MATLAB. The damping of glass-fiber reinforced plastic beam element vibrations is considered in this paper as the numerical example. The parameters of nonlocal model are determined with the least squares method using numerical simulation data obtained in SIMULIA Abaqus CAE. The advantage of flexible nonlocal damping model over the local one (Kelvin-Voight model) is shown for the orthotropic beam vibration simulation in cases when the one-dimensional models are preferable.