One of the most important challenges in the field of structural health monitoring and non-destructive testing is to assess some features of damages in structures, like the shape of damaged region. To reconstruct the shape of damage there are different methods in tomography. Already, researchers have used two general types of shape reconstruction techniques: transform based methods and algebraic reconstruction methods. Both methods suffer from some disadvantages like high sensitivity to incomplete data sets, bulky and expensive scanning hardware or low image resolution. In this work, a novel method to find the shape of damage via polygon reconstruction technique in tomography using the Radon transform is introduced. In this technique, damaged region is approximated by a polygon which the number of its sides is chosen arbitrarily, and the aim is to find this polygon’s vertices. To achieve this goal, an aluminum plate with a triangular hole as the damage was modeled in software. Then beams of guided Lamb wave were propagated toward the damaged region using arrays of piezoelectric transducers in just a few numbers of angles. Finally the polygon’s vertices were determined by processing the reflected signals from the damaged region. The results confirmed the efficiency of the proposed method.