Within　the　realm　of　structural　reliability　analysis,　the　uncertainties　tied　to　resistance　and　loads　are　conventionally　embodied　as　random　variables　possessing　established　cumulative　distribution　functions　(CDFs).　Nevertheless,　real-world　scenarios　often　involve　cases　where　the　CDFs　of　random　variables　are　unknown,　necessitating　the　probabilistic　traits　of　these　variables　solely　through　statistical　moments.　In　this　study,　for　the　purpose　of　integrating　random　variables　characterized　by　an　unknown　CDF　into　the　framework　of　Monte　Carlo　simulation　(MCS),　a　linear　moments　(L-moments)-based　method　is　proposed.　The　random　variables　marked　by　an　unknown　CDF　are　rendered　as　a　straightforward　function　of　a　standard　normal　random　variable,　and　the　formulation　of　this　function　is　determined　by　utilizing　the　L-moments,　which　are　typically　attainable　from　the　statistical　data　of　the　random　variables.　By　employing　the　proposed　approach,　the　generation　of　random　numbers　associated　with　variables　with　unknown　CDFs　becomes　a　straightforward　process,　utilizing　those　derived　from　a　standard　normal　random　variable　constructed　by　using　Box-Muller　transform.　A　selection　of　illustrative　examples　is　presented,　in　which　the　efficacy　of　the　technique　is　scrutinized.　This　examination　reveals　that　despite　its　simplicity,　the　method　demonstrates　a　level　of　precision　that　qualifies　it　for　incorporating　random　variables　characterized　by　unspecified　CDFs　within　the　framework　of　MCS　for　purposes　of　structural　reliability　analysis.　Copyright　©　2024　by　ASME.