With the method of LEED graphic fitting, we have made a thorough study on the stability and faceting of In/Si surfaces. As a result, three new In/Si stable surfaces with less than 0.5 ML coverage ,that is, Si(2 1 4)-In, Si(3 1 7)-In and Si(4 3 6)-In and two In/Si stable surfaces with about 1ML coverage, that is, Si(1 0 1)-In and Si(3 1 3)-In, have been found. Meanwhile, the family territories of total 4 In/Si stable surfaces with less than 0.5 ML coverage and 6 with about 1ML coverage have been roughly determined. Particulaty, the family territory of Si(1 0 3)-In is rather big, even a little bigger than that of Si(1 1 1)-In.