The　value　of　slope　of　a　grid　derived　from　DEM　varies　with　the　resolution　of　DEM.　The　pattern　of　the　slope　variation　is　meaningful　for　the　deep　understanding　of　the　general　variation　rule　of　slopes.　The　mathematical　model　for　deriving　slopes　was　analyzed,　and　the　real　data　were　used　to　test　it.　The　following　conclusions　are　obtained:　as　the　resolution　of　DEM　becomes　rough,　the　increase　and　decrease　of　the　slope　value　depends　upon　the　first　order　partial　derivative,　the　three　partial　derivative　and　the　mixed　three　partial　derivative　of　the　function　of　real　surface;　as　the　resolution　of　DEM　is　less　than　30　meters,　(1)　the　amount　of　grids　with　minus　sign　of　slope　error　is　about　7　times　more　than　that　of　grids　with　plus　sign　of　slope　error,　and　the　absolute　value　of　minus　error　is　over　2　times　as　much　as　that　of　plus　error,　(2)　plus-or-minus　sign　of　slope　error　is　not　related　to　the　resolutions　of　DEM,　and　(3)　it　is　the　absolute　value　of　minus　error　that　is　more　sensitive　to　the　change　of　the　resolutions　of　DEM　than　the　value　of　plus　error.　The　research　method　was　put　forward　to　analyse　the　sensitivity　of　error.　The　researchers　have　got　the　formulas　for　calculating　slope　errors　from　the　resolutions　of　DEM　or　from　the　averages　of　slope.　The　formulas　would　provide　the　guidance　for　the　practical　application　departments.