This paper presents a finite element formulation for the seismic response of damped structural systems. Damping is obtained using a viscoelastic material, which is characterized by a constitutive law with fractional derivatives. The weighted residue method is applied resulting in a fractional motion equation, which is numerically integrated through an implicit scheme in combination with the constant acceleration Newmark method. An example of application is presented, in which the response of a cantilever beam with free layer damping is analyzed. The material properties are identified from the material experimental characterization, where the parameters of the fractional model were identified by curve fitting. The results of the simulation are compared with the experimental ones, concluding that the tendencies observed in the measurements are reproduced.