Structures with non-conservative loads can lose stability either by divergence, when static response amplitude increases monotonically, or by flutter, through oscillations with exponentially increasing amplitudes. Several aspects concerning the influence of damping and shear on the dynamic stability of beams and tubes are studied. A special-purpose computer program has been developed, enabling critical loads and time history responses to be obtained applying the finite element method to formulation of the equations. Results of Euler-Bernoulli and Timoshenko beams are compared for a number of alternative formulations of proportional and viscoelastic damping. Tubes are modeled with tridimensional elements implemented with additional incompatible modes. Viscoelastic damping is introduced in the constitutive relations of the material, acting on deviatoric strains. Flutter loads are calculated through the characteristic eigenvalue problem obtained applying the Laplace’s transform to the momentum equation. In the dynamic analysis an implicit method is used for time integration and a second order algorithm is used in the integration of viscoelastic constitutive relations. The results show that, for some types of damping, the responses obtained taking into account shear strains change qualitatively the behavior of the flutter load, including certain paradoxical phenomena, as damping is increased.