Centerless grinding is one of the most productive machining methods and is used in the mass production of automotive parts and rolling bearings. Shoe-type centerless grinding allows precise machining of the outer and inner shaped surfaces of bearing rings. Reducing tolerances on the size and shape of bearing parts requires improved centerless grinding. The most difficult thing is to ensure the roundness is less than 1 mm. This requires the development of mathematical models of a high degree of adequacy. This paper presents a new estimation method for geometric stability based on computer simulation. A mathematical model of centerless location on shoes with the high degree of adequacy to the real process has been developed. The main innovations of the developed method were a numerical algorithm for searching for points of contact between the part and the shoes and equation for determining the center of the part as the point of intersection of the trajectory of its movement along the opposite shoes. Based on computer modeling, the trajectories of movement of the profile points were studied and the patterns of geometric stability were established. An evaluation indicator is proposed in the form of the maximum trajectory error of the profile point during one full turn of the part. The possibility of optimizing machining by setting up shoe angles has been confirmed. Experimental verification confirmed high geometric stability due to the shoes location according to the new model.