There are a number of problems in mechanical engineering technology. One of them is related to the installation on the machine and the previous processing of thin-walled rings, which are widely used in mechanical engineering. Due to the low bending stiffness of thin-walled rings after processing there are a large magnitude of rigidity of the form (deviation from roundness). As production experience has shown, in the conditions of mass production, it is advisable to use fungal mandrels and adjustments to reduce shape errors. They allow for a small radial gap between the holes of the ring and the fungal cam to have extended contact rings with cams along the angular coordinate. However, there are no methods for calculating the parameters of contact interaction with cams, considering a number of factors, primarily the radial clearance. Hence, it is impossible to calculate more accurately the error of the form after processing. In this paper (it is supposed to be continued), based on methods for calculating flat rings of construction mechanics of machines, a method for determining the stress-strain state of a thin-walled state is proposed, considering the contact pressure. In this case, the semiangle of contact of the ring with the fungal cam and the shape of the contact pressure plot are determined. This allows you to calculate the stress state of the thin-walled ring and the shape error when processing more accurately in a fungal mandrel, as well as reasonably assign the dimensions of the mandrel parts. Due to the exceptionally large number of calculations in the calculations according to the proposed method, it can only be implemented using a computer program, which creates great difficulties in analyzing different source data. Therefore, it is planned to rework the completed developments into an engineering calculation method with graphs in dimensionless form.