This paper discusses the formulation and solution for the problem of damped transverse vibrations of the Γ type frame with open cracks. Dissipation of vibration energy in the frame results from the movement constraint in the column and bolt support (constructional damping) and internal damping of viscoelastic material of the frame (rheological model by Kelvin-Voigt). Presence of a crack impacts local flexibility that has an effect on frame vibration response. The boundary problem for the above system was formulated based on the Hamilton’s principle and solved numerically for the complex eigenvalues ω*. The effect of the crack depth and its location on damped vibration was presented. The effect of both types of damping on the degree of amplitude decay was also presented
