Resonance damping for a vibrating plate is investigated both according to the exact equations of dynamical viscoelasticity and the classical thin‐plate equations derived in mechanics of materials. The plate is assumed as isotropic and homogeneous and no shear‐ or rotatory‐inertia corrections have been included in the thin‐plate approximations. Two types of materials are investigated that correspond to real and complex values of the bulk modulus. For each case, the complex shear modulus is μ(1+ig) and values ofgup to 0.10 were used in the calculations. The two theories are in excellent agreement in a range of wavelengths as low as about ten times the thickness. It is found that thin‐plate theory evaluates the damping more accurately than it does the static rigidity.