When　considering　initial　stress　field　in　geomaterial,　nonzero　resultant　of　shallow　tunnel　excavation　exists,　which　produces　logarithmic　items　in　complex　potentials,　and　would　further　lead　to　a　unique　displacement　singularity　at　infinity　to　violate　geo-engineering　fact　in　real　world.　The　mechanical　and　mathematical　reasons　of　such　a　unique　displacement　singularity　in　the　existing　mechanical　models　are　elaborated,　and　a　new　mechanical　model　is　subsequently　proposed　to　eliminate　this　singularity　by　constraining　far-field　ground　surface　displacement,　and　the　original　unbalanced　resultant　problem　is　converted　into　an　equilibrium　one　with　mixed　boundary　conditions.　To　solve　stress　and　displacement　in　the　new　model,　the　analytic　continuation　is　applied　to　transform　the　mixed　boundary　conditions　into　a　homogenerous　Riemann-Hilbert　problem　with　extra　constraints,　which　is　then　solved　using　an　approximate　and　iterative　method　with　good　numerical　stability.　The　Lanczos　filtering　is　applied　to　the　stress　and　displacement　solution　to　reduce　the　Gibbs　phenomena　caused　by　abrupt　change　of　the　boundary　conditions　along　ground　surface.　Several　numerical　cases　are　conducted　to　verify　the　proposed　mechanical　model　and　the　results　strongly　validate　that　the　proposed　mechanical　model　successfully　eliminates　the　displacement　singularity　caused　by　unbalanced　resultant　with　good　convergence　and　accuracy　to　obtain　stress　and　displacement　for　shallow　tunnel　excavation.　A　parametric　investigation　is　subsequently　conducted　to　study　the　influence　of　tunnel　depth,　lateral　coefficient,　and　free　surface　range　on　stress　and　displacement　distribution　in　geomaterial.　©　2023　Elsevier　Inc.