Based on the Mogi–Coulomb criterion, the elastic–plastic analysis of the ideal elastic–plastic adjoining rock mass of a non-circular tunnel with pressures in two directions was performed using complex variable function theory and the stress construction method. The analytical expressions of the radius of the non-circular plastic zone and the radial displacement of the tunnel wall were obtained by a mapping function, and the solutions were examined using engineering examples. The results showed that the intermediate principal stress caused the radius of the plastic zone and the displacement of the tunnel wall to change symmetrically. The increase in the lateral pressure coefficient changed the shape of the plastic zone. The radius of the plastic zone of the tunnel roof and the floor increased, and the displacement of the plastic zone of the two sides of the tunnel decreased. The displacement of the tunnel wall increased first and then decreased at 0° of the inner boundary angles of the tunnel, and it increased at other angles. Therefore, this paper provides a scientific basis for the design of two-way unequal-pressure non-circular tunnel supports, and it has certain guiding significance for engineering practice.