Over-break　and　under-break　excavation　is　very　common　in　practical　tunnel　engineering　with　asymmetrical　cavity　contour,　while　existing　conformal　mapping　schemes　of　complex　variable　method　generally　focus　on　tunnelling　with　theoretical　and　symmetrical　cavity　contour.　Besides,　the　solution　strategies　of　existing　conformal　mapping　schemes　for　non-circular　tunnel　generally　apply　optimization　theory　and　are　thereby　mathematically　complicated.　This　paper　proposes　a　new　bidirectional　conformal　mapping　for　over-break　and　under-break　tunnels　of　asymmetrical　contours　by　incorporating　Charge　Simulation　Method,　which　only　involves　a　pair　of　forward　and　backward　linear　systems,　and　is　therefore　logically　straightforward,　computationally　efficient　and　practically　easy　in　coding.　New　numerical　strategies　are　developed　to　deal　with　possible　sharp　corners　of　cavity　by　small　arc　simulation　and　densified　collocation　points.　Several　numerical　examples　are　presented　to　illustrate　the　geometrical　usage　of　the　new　bidirectional　conformal　mapping.　Furthermore,　the　new　bidirectional　conformal　mapping　is　embedded　into　two　complex　variable　solutions　of　under-break　shallow　tunnelling　in　gravitational　geomaterial　with　reasonable　far-field　displacement.　The　respective　result　comparisons　with　finite　element　solution　and　existing　analytical　solution　show　good　agreements,　indicating　that　the　new　bidirectional　conformal　mapping　would　extend　the　mechanical　application　range　of　the　complex　variable　method　in　practical　over-break　and　under-break　tunnelling.