The paper addresses the analytical determination of vibrodiagnostic parameters that describe the presence of normal-rupture flat through-the-thickness and surface semi-elliptical central cracks in a rectangular homogeneous plate of constant thickness for various plate fixing conditions and vibration modes. It is shown that the most sensitive vibrodiagnostic damage parameter of a plate is the variation of the logarithmic decrement in the case of a through-the thickness crack and the second-harmonic ratio of the vibration process in superharmonic resonance in the case of a surface crack.