Most of the failures that cause serious damage to the structures can be attributed to cracks. Cracks may arise during manufacturing or usage of structuresor can occur during environmental conditions.The tiny cracks that are created may join together and form larger cracks.Crack in a structure introduces local flexibility and changes stiffness and dynamic behavior of the structure. Cracks present a serious threat to the performance of the beam-like structures Many studies have been done on the identification of the cracklocation and depth, using vibration parameters of the structures. The objective of any damage assessment technique is to inquire whether any structural damage, such as the initiation of a crack has occurred, and if so, to determine its specifications.As we know the natural frequencies of an object depends on the shape, material and density of the object. There are many parameters that effect on the dynamic behavior of a structure. Determination of such parameters for determining the reliability is one of the major problems in engineering structures.Crack detection based on modal frequency has been a common and widely used approach. In this paper, the flexural vibration of a cantilever taper beam having a transverse crack is considered. The beam natural frequencies are obtained for various crack locations and depths and beam angles, using the finite element method. These natural frequencies and crack specifications are then used to train a neural network. The input of the neural network is three natural frequencies of the beam and taper beam angle and the output is the crack specifications. Simulations are performed to evaluate performance of the neural network. Results show that the proposed scheme can detect transverse cracks in taper cantilever beams with good accuracy. To train the neural network, many actual sets of input-output data are required. The actual data are obtained using the finite element method via Abaqus software for a number of cracks with different specifications. To determine different specifications of the crack, full factorial design is employed The full factorial design which is a comprehensive method and considers the effects of original factors is used in this study. Keywords: Taper beam, Transverse crack, Natural frequency, Fullfactorial design, Neural network