Most of the failures that cause serious damage to the structures can be attributed to cracks. Crack in a structure introduce local flexibility and changes in the stiffness and dynamic behavior of the structure. Many studies have been done on identification of the crack location 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. Crack detection based on modal frequency has been a common and widely used approach. Cracks present a serious threat to the performance of beam-like structures. In this paper, the flexural vibration of a cantilever beam having a slant crack is considered. The beam natural frequencies are obtained for various crack locations, depths and 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 the crack specifications and the output is five natural frequencies of the beam. With the trained neural network, genetic algorithm is then used to determine the beam crack specifications by minimizing the differences from the measured frequencies. Simulations are performed to evaluate performance of the neural network. Results show that the proposed scheme can detect slant cracks in cantilever beams with good accuracy. Buckling is defined as the change of equilibrium state of a column or rod from one configuration to another at a critical compressive load. In columns, the maximum compressive load that the column can carry is usually limited by the buckling phenomenon. In the second part of the thesis buckling load of a column having a slant crack is obtained by using a proposed scheme. Two main approaches are usually used for detecting buckling load: destructive and non-destructive methods. In destructive method the compressive load is applied to the structure until it will be buckled. Today, neural network (NN) is used as a non-destructive method for predicting buckling load. In this study a fixed-free column having a slant crack with three specifications: location (L), depth (D) and angle (?), is considered. A scheme that its inputs and output are respectively five natural frequencies and the buckling load of the cracked column is proposed. This scheme includes neuro-genetic technique and one separate neural network. At first, the neuro-genetic technique detects the specifications of the crack of the column and then the neural network predicts the buckling load of the column having a slant crack with these specifications. Results show that the proposed scheme can precisely detect buckling load in columns. The column and the beam that are considered in this study have similar shape and material properties so results of beam crack specifications can be used for detecting column crack specifications. 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 Ansys 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 is a comprehensive method which considers the effects of original factors. Keywords: Slant crack, Natural frequency, Buckling load, Full factorial design, Neural network, Genetic algorit