An offset of roller cone rotation centerlines is used to increase the mechanical penetration rate while drilling in soft rocks. This enables increasing the area of a cutting structure teeth contact with a bottom hole. The analysis of offset cone drill bit (cutting structure) teeth wear showed that particularly significant wear is characteristic of the transition zone from the heel cone to the nose cone; which leads to significant reduction in the mechanical rate of penetration and a rapid decrease in the hole diameter. The purpose of this paper is to conduct a theoretical research on the nature and conditions of interaction between heel and peripheral nose cones of offset roller cone bits with a bottom hole; which is aimed at improving the efficiency of rock cutting by offset roller cone bits. To achieve the purpose; the authors analyzed data on the nature and causes of wear of existing offset roller cone bit cutting structure (teeth); developed a mathematical model in a cylindrical coordinate system allowing to determine the location and geometric parameters of the gage cone contact area with the hole wall for different roller cone bits sizes; developed a computer solid model for checking the adequacy of the mathematical model by comparing these two models; prepared recommendations for further improvement of the design of existing offset roller cone bit cutting structure (teeth). The research was carried out by the method of mathematical simulation of geometric figures and bodies corresponding to roller cones and a hole. The research has revealed that significant adjustments need to be made to the geometry of the roller cone teeth (currently being patented). This would allow decreasing the areas of cone heel blunting by 15–20 % as well as providing more prolonged contact of base and gage cones with bottom hole and wall surfaces. This allows to reduce wear of teeth in the transition zone of the generatrix from the peripheral nose cone to the gage (heel) cone of the roller cone and to maintain the required specific pressure on the cut rock for a longer period of time and; as a result; to increase both the mechanical penetration rate and the service life of the drilling tools.