Two 2-D aeroelastic models are presented here to determine instability boundary (flutter speed) and gust response of a typical section airfoil with degrees of freedom in pitch and plunge directions. To build these 2-D aeroelastic models, two different aerodynamic theories including Indicial Aerodynamic Theory and Vortex Lattice Method (VLM) have been employed. Also, a 3-D aeroelastic framework constructed of Boundary Element Method (BEM) and modal technique is used to show the accuracy and reliability of the presented 2-D aeroelastic models. The methods reviewed in this study are used to predict the non-dimensional flutter speed and its corresponding frequency for a typical section airfoil (for the 3-D model a high aspect ratio wing with the same cross-sectional characteristics is used) Then, a group of figures show how different time-marching schemes can change the dynamic responses due to the sharp edge gust. Also, a set of figures provide some comparisons between the 2-D aeroelastic models, and also, with the 3-D model. As seen from the results presented in this study 2-D aeroelastic models give lower non-dimensional flutter speed than the 3-D model. In addition, the dynamic responses due to the sharp edge gust predicted by the 2-D models show larger amplitudes than the 3-D model. It means that since the 2-D aeroelastic models can overestimate the dynamical behavior such as flutter speed and responses to the sharp edge gust, they can be used in the preliminary design steps to reduce the cost and save time.