A　stochastic　finite　element　method　based　on　B-spline　wavelet　on　the　interval　(BSWI-SFEM)　is　presented　for　static　analysis　of　1D　and　2D　structures　in　this　paper.　Instead　of　conventional　polynomial　interpolation,　the　scaling　functions　of　BSWI　are　employed　to　construct　the　displacement　field.　By　means　of　virtual　work　principle　and　BSWI,　the　wavelet　finite　elements　of　beam,　plate,　and　plane　rigid　frame　are　obtained.　Combining　the　Monte　Carlo　method　and　the　constructed　BSWI　elements　together,　the　BSWI-SFEM　is　formulated.　The　constructed　BSWI-SFEM　can　deal　with　the　problems　of　structural　response　uncertainty　caused　by　the　variability　of　the　material　properties,　static　load　amplitudes,　and　so　on.　Taking　the　widely　used　Timoshenko　beam,　the　Mindlin　plate,　and　the　plane　rigid　frame　as　examples,　numerical　results　have　demonstrated　that　the　proposed　method　can　give　a　higher　accuracy　and　a　better　constringency　than　the　conventional　stochastic　finite　element　methods.