An important class of problems in the field of geotechnical engineering may be analyzed with the aid of a simple integro-differential equation. Behavior of "rigid" piles(say concrete piles), "deformable" piles(say gravel piles), pile groups, pile-raft foundations, heavily reinforced earth, flow within circular silos and down drag on cylindrical structures (for example the crusher unit of a mineral processing complex) are the type of situations that can be handled by this type of equation. The equation under consideration has the form; $$frac{{partial}w(r,;z)}{{partial}z}+f(z){int}^z_0g({xi})(frac{{partial}^2w(r,;{xi})}{{partial}r^2}+frac{1}{r}frac{{partial}w(r,;{xi})}{{partial}r})d{xi}+h(r,;z)=0$$ where w(r, z) is the vertical displacement of a soil particle expressed as a function of the polar cylindrical space coordinates (r, z) and the symbols f, g and h represent soil properties and the loading conditions. The merit of the analysis is its simplicity (both in concept and in application) and the ease with which it can be expressed in a computer code. In the present paper the analysis is applied to investigate the behavior of a single rigid pile to bedrock. The emphasis, however, is placed on developing the equation, the numerical techique used in its evaluation and validation of the technique, hereafter called the ID technique, against a formal program, CRISP, which uses the FEM.