Over-/under-break　excavation　is　a　common　phenomenon　in　shallow　tunnelling,　which　is　nonetheless　not　generally　considered　in　existing　complex　variable　solutions.　In　this　paper,　a　new　equilibrium　mechanical　model　on　over-/under-break　shallow　tunnelling　in　gravitational　geomaterial　is　established　by　fixing　far-field　ground　surface　to　form　a　corresponding　mixed　boundary　problem.　With　integration　of　a　newly　proposed　bidirectional　composite　conformal　mapping　using　Charge　Simulation　Method,　a　complex　variable　solution　of　infinite　complex　potential　series　is　subsequently　derived　using　analytic　continuation　to　transform　the　mixed　boundaries　into　a　homogenerous　Riemann–Hilbert　problem,　which　is　iteratively　solved　to　obtain　the　stress　and　displacement　in　geomaterial.　The　infinite　complex　potential　series　of　the　complex　variable　solution　are　truncated　to　obtain　numerical　results,　which　is　rectified　by　Lanczos　filtering　to　reduce　the　oscillation　of　Gibbs　phenomena.　The　bidirectional　conformal　mapping　is　discussed　and　validated　via　several　numerical　cases,　and　the　subsequent　complex　variable　solution　is　verified　by　examining　the　Lanczos　filtering　and　solution　convergence,　and　comparing　with　corresponding　finite　element　solution　and　existing　analytical　solutions.　Parametric　investigation　is　conducted　to　illustrate　possible　usage　of　the　proposed　analytical　solution.　Further　discussions　are　made　to　disclose　possible　defects　of　the　proposed　solution　for　objectivity.　©　2024　Elsevier　Ltd