This document has developed both the strategy and equations necessary to understand the stress distribution when two conical shaped rollers come into contact, both over their contact surface region and inside the material. One of the most important findings of this thesis is that when two conical rollers push against one another, the resulting contact patch takes a trapezoidal-like shape due to the geometry of the cone and the type of loading. As a direct result of the geometry of the cone, the contact patch is smallest at the smallest cross-sectional area and largest at the largest cross-sectional area. Nevertheless, the stress magnitude is largest at the smallest cross-section and gradually decreases until it reaches the smallest stress value at the largest cross-section. The maximum stress on the cone's surface is located at the center of the contact patch of a given section. As the measured points move away from the center of the contact patch, the stress distribution across the contact patch gradually drops. Once the measured points are outside the contact patch, where the distance from the center of the contact patch is greater that the contact patch half-width, the stress distribution takes an abrupt change. This change will drop until eventually the measured stress reaches zero when points are calculated a fair distance away from the contact region.