Abstract: In the crack growth analysis, the Stress Intensity
Factor (SIF) is a fundamental prerequisite. In the present study, the
mode I stress intensity factor (SIF) of three-dimensional penny-
Shaped crack is obtained in an isotropic elastic cylindrical medium
with arbitrary dimensions under arbitrary loading at the top of the
cylinder, by the semi-analytical method based on the Rayleigh-Ritz
method. This method that is based on minimizing the potential
energy amount of the whole of the system, gives a very close results
to the previous studies. Defining the displacements (elastic fields) by
hypothetical functions in a defined coordinate system is the base of
this research. So for creating the singularity conditions at the tip of
the crack the appropriate terms should be found.