A　new　static　equilibrium　mechanical　model　on　noncircular　shallow　tunnelling　considering　initial　stress　field　is　proposed　in　this　paper　by　constraining　far-field　ground　surface,　and　a　mixed　boundary　value　problem　thus　forms　with　elimination　of　displacement　singularity　at　infinity.　By　applying　analytic　continuation,　the　mixed　boundaries　are　transformed　to　a　homogeneous　Riemann–Hilbert　problem,　which　is　subsequently　solved　via　an　efficient　and　accurate　iterative　method　with　boundary　conditions　of　static　equilibrium,　displacement　single-valuedness,　and　traction　along　tunnel　periphery.　The　Lanczos　filtering　technique　is　used　in　the　final　stress　and　displacement　solution　to　reduce　the　Gibbs　phenomena　caused　by　the　constrained　far-field　ground　surface　to　obtain　more　reasonable　results.　Several　numerical　cases　are　conducted　to　intensively　verify　the　proposed　solution　by　examining　the　utilization　of　Lanczos　filtering,　the　elimination　of　displacement　singularity,　and　solution　convergence　of　constraining　arc　and　truncation　number,　and　comparisons　with　existing　solutions,　and　all　the　results　are　in　good　agreements.　Finally,　more　numerical　cases　are　conducted　to　investigate　the　stress　and　deformation　distribution　along　ground　surface　and　tunnel　periphery　considering　different　tunnel　geometries,　lateral　coefficients,　and　tunnel　depths.　Further　discussions　on　the　defects　of　the　proposed　solution　are　also　conducted　for　objectivity.　©　2023　Elsevier　Ltd