The theory of slope erosion is developed along similar lines to the theory of heat flow in solid added to the correcting factor. if slope erosion in the forest and grassland proceeds according to the hypothesis, it is $delta$y $delta^2$y = k $delta^2$y $delta$$X^2$+f(s b. t) where 5 is internal properties of slope soil and b is biota on slope. When the variables of the equation of slope erosion are x = -λ the initial elevation=-f(λ), x=λ, x==a, the steady value of the initial elevation=y, and dy dx x=0> =O(t>o), respectively, the houndary condition due to the solution of the equation of slope erosion is y= 2 √$pi$kt [∫a o λe $(X-λ)^2$4kt dλ- ∫ao- $(x+λ)^2$4kt dλ] + ∫∫∫ f (s.b. t)dtdbds Key words: Theoretical analyses, Soil erosion and conservation, Slope erosion