In this project, Green’s function method is applied to obtain analytic solutions for regular and singular type of Sturm-Liouville’s problems with Bessel’s equation, Euler equation, Legendre equation, Chebesheve equation and Hermite equation by using Green’s function method. Applications of the method are illustrated by examples for various Sturm-Liouville problems with most important boundary conditions, namely, Dirichlet, Neumann and mixed boundary conditions