Plates have been extensively used in airplanes, spaceships, missiles, machines, surface vessels, submarines and storage tanks in the past decade. Considerable progress in material science and engineering and increasing demands for lighter and stiffer structures leading the researchers to make composites and functionally graded materials (FGM). Complex dynamic response and chaotic behavior of plates has been recently considered by many researchers around the world. This complex dynamic response of plates occurs under large amplitude forces. In this thesis, nonlinear chaotic vibration behavior of a cylindrical shell made of functionally graded material (FGM) is investigated. Material properties vary along the shell thickness according to power law based on the volume content of the constituent which are a metal and a ceramic. Material properties are also temperature dependent. Loading is a combination of distributed static and harmonic exciting forces in axial and radial directions in the presence of a temperature gradient in radial direction. The cylindrical shell is assumed to be simply supported. Donnel’s nonlinear shell theory is used for cylindrical shell equations. Using Airy stress function, equations of motion are written in terms of radial displacement and stress function. Selecting suitable displacement function and using Galerkin method nonlinear differential equations are changed into ordinary differential equations. These are three differential equations containing second and third order nonlinear terms. Using Runge-kutta 4th order method the equations of motion are solved. In order to recognize nonlinear behavior of the system, techniques such as time histories, phase diagram, power spectrum, Poincare map, bifurcation diagrams and maximum Liapanov exponents are employed. In this research effect of parameters such as frequency ratio, temperature gradient, uniaxial and biaxial exciting forces and the material inhomogeneity exponent is investigated. The results indicate that some parameters such as temperature gradient and axial static force have significant effect on chaotic behavior of the cylindrical shell. The results of this research are validated with the existing literature. Moreover, in this thesis, nonlinear dynamic response of the cylindrical shell under radial exciting force is also investigated using multiple scale method. The solution is done near resonance and the effect of parameters such as thickness, temperature, FGM exponent and axial static force are considered. The results in this case indicate that increasing temperature and axial static force soften the shell behavior while increasing thickness can cause stiffening of the structure. The results of this case are in good agreement with other researcher results. Keywords : Cylindrical shell, functionally graded material (FGM), multiple scale method, maximum Lyapunov exponents, chaotic behavior