This　study　provides　semi-analytical　solutions　for　the　cylindrical　cavity　expansion　(CCE)　problem,　utilizing　the　non-orthogonal　elastoplastic　clay　(NEPC)　model.　The　analysis　covers　both　undrained　and　drained　scenarios.　The　NEPC　model　captures　the　soil＇s　softness/hardness　and　volume　change　behavior　using　only　a　fractional　order　parameter,　without　requiring　an　additional　plastic　potential　function.　After　a　brief　introduction　to　the　NEPC　model,　we　derive　solutions　by　solving　a　system　of　closed-form　ordinary　differential　equations　that　involve　the　material　derivative　of　effective　stresses.　The　presented　semi-analytical　solutions　are　validated　through　finite　element　(FE)　solutions　which　are　obtained　on　an　implicit　unconstrained　stress　update　algorithm.　The　impact　of　the　fractional　order　on　the　expansion　process　is　analyzed　and　discussed　in　depth,　covering　the　normal　and　overconsolidated　soils.　The　presented　solutions　provide　a　framework　for　analyzing　CCE　in　clay,　considering　the　softness/hardness　and　volume　change　behavior　of　the　soil,　and　can　act　as　a　benchmark　for　validating　numerical　solutions　for　non-orthogonal　elastoplastic　models.