The problem of dissipating energy in structures is becoming an important consideration in mechanical design. In this paper, the bending vibrations of Euler-Bernoulli beams treated with non-local viscoelastic damping patches have been studied. The non-local viscoelastic properties of the damping patch can be represented by a spatial kernel function and a relaxation function, respectively, and the corresponding equation of motion of the beam has been solved using the Galerkin method in the Laplace domain, following the procedure previously proposed by other authors. A parametric study has been conducted to analyze the influence of different parameters involved in the model, and a damping capacity function has been defined for this purpose.