Single-mode　waveguiding　devices　are　desired　for　photonic　integrated　circuits.　Previous　studies　on　the　single-mode　conditions　(SMCs)　of　a　silicon-on-insulator　(SOI)　rib　waveguide　lack　a　comprehensive　discussion　to　include　a　large　to　small　range　of　cross-section　cases,　thus　revealing　the　discrepancies　of　various　determination　methods.　Here,　we　reanalyze　the　SMCs　for　large　and　small　SOI　rib　waveguides　by　utilizing　a　finite-element　method　mode　solver.　The　results　are　compared　with　both　classical　SMCs　of　Soref＇s　expression　and　Pogossian＇s　effective-index　method,　indicating　that　the　constant　value　a　shown　in　the　Soref＇s　analytical　expression　depends　on　the　rib　heights　and　polarizations.　For　transverse-electric　polarized　light　and　the　waveguide　height　exceeding　5　mu　m,　alpha　is　approaching　that　of　Soref＇s　equation;　if　the　height　is　＜=　5　mu　m,　then　alpha　=　0.35,　0.4,　0.45,　0.7,　and　1.0　are　determined　for　the　cases　of　5,　3,　2,　0.8,　and　0.4　mu　m　heights,　respectively.　However,　for　transverse-magnetic　polarized　light,　if　the　height　＞=　2　mu　m,　alpha　is　constant　(0.25)　and　independent　on　the　rib　heights,　and　alpha　=　0.18　and　0.12　are　attained　for　the　cases　of　0.8　and　0.4　heights,　respectively.　This　detailed　analysis　indicates　that　a　wider　rib　width　can　be　used　while　preserving　a　SMC　leading　to　devices　with　improved　coupling　efficiencies　and　reduced　insertion　losses　for　on-chip　photonic　circuits.