The paper presents the results of a study to determine the stress state on the contours of underground workings, the cross-section of which has the form of an ellipse with a fixed value of the large semi-axis. For workings of this type, at different values of the ellipse parameter, the permissible depths of laying and the values of uniform pressure at the points of their contours are determined, at which normal tangential stresses do not exceed the tensile and compressive strength limits of the host rock. Based on the strength condition used in the work, the values of the permissible depths of the workings are calculated for varying values of uniform pressure applied at the points of the workings contours and the specified values of the lateral expansion coefficient of the rock. The permissible values of the stretching uniform pressure at the points of the contours of the elliptical shape of the cross-section with a change in the depth of laying, the specified values of the lateral expansion coefficient of the rock and the ellipse parameter are given. In addition, the paper presents formulas on the basis of which the problem of stress distribution at the points of contours whose cross-section has the shape of an ellipse with a fixed value of the large semi-axis is considered. It is established that when the intensity of the stretching uniform pressure applied at the points of the contours of the workings of an elliptical cross-section shape changes, and the specified values of the ellipse parameter, the depth of the workings and the magnitude of the lateral expansion coefficient of the host rock, sections of the contours on which tensile and compressive stresses act are highlighted. When changing the depths of the workings of the elliptical cross-section shape, sections of contours are identified on which tensile and compressive stresses act at given values of the ellipse parameter, the intensity of the stretching uniform pressure applied to the points of the contours, and the values of the lateral expansion coefficient of the rock.