Using the variables - separated method under the polar coordinate system，the normal modes of analytical solution of small flexivity vibration equation on a sectorial thin plate along the vertical direction is studied experimentally and theoretically when the boundary is free.The radii of arc-shaped standing wave nodes on the thin plate are calculated exactly for different frequencies，the laws of equation’s eigen-values and the modulus of plate are obtained.The figures of standing waves are also plotted.Two kinds of standing wave nodes are observed on the board: only radical nodes and both of arc - shaped and radical shape nodes. The theoretical results are in well agreement with the experimental measurements.