In this research approximate solutions are developed to solve Functionally Graded Material (FGM) beam and column problems. FGM is considered in the transversal direction of both beams and columns using different functions; power function, exponential function, and sigmoidal function. Also, different power values are used to consider different material concentrations in the transversal direction of beams and columns. Approximate solutions are first developed for FGM beams using iterative techniques based on averaging the elasticity modulus in beam's tension and compression zones to determine different structural outputs like deflection, slope, shear and moment diagrams. Then outputs are compared to classical Euler bending theory to validate the adopted approximate method used in the solution. In addition to beam bending problems, approximate solutions for FGM column buckling problems are also developed. The methods adopted in solution are Rayleigh's Quotient, Timoshenko's Quotient, and Rayleigh-Ritz method. These methods are compared to the analytical classical Euler buckling solution. MATLAB program is adopted to solve both problems since it is simple and precise. The main results of this study shed the light on the importance of approximate solutions in solving FGM bending and buckling problems. For bending problems, the approximate method suggested resulted in trivial error (~0%) when compared to analytical solution. As for buckling problems, Rayleigh-Ritz method showed to be the most accurate one in calculating critical buckling load with error less than 0.75%, while Rayleigh method led to significant errors (~22%). At the end of this work, some recommendations were presented for future research work on FG structural members. Keywords: Functionally Graded Materials, Bending of Beams, Buckling of Columns, Approximate solution.