The problems of ensuring reliability and improving the drilling of exploratory wells on the shelf from monopod bases are investigated. The analysis of static and dynamic strength of mono-support bases under different technical and marine hydrological conditions is performed. Engineering methods for practical calculations of monopod bases and selection of their optimal parameters are proposed. A new drilling rig “Start” designed for offshore drilling from mono-supported bases is designed and manufactured. Introduction of such technology will allow us to develop oil and gas fields in the seas of our motherland. These areas are the most promising for the search of unique and giant hydrocarbon deposits.