Planar half spaces are fundamental in analysis structure. However many mathematical method used to solve the equation associated with those structure their applicability. Finding a solution usually requires a solution process where the form of a solution is assumed so that governing equation are satisfied. This process is usually accomplished with the help of an Airy stress function that is determined based on a few assumptions about the relationship between the stress function and the true stress. The process is tedious and often a single solution that is valid for a single. In this work we represent a general solution to a bi harmonic equation using Fourier series that works for a variety of boundary condition in polar coordinates. This function is simplified with minor assumption about its form and solved analytically. A representative problem and its solution is also shown.