Research conclusions :(1) A search pattern which is based on the hypothesis of combination sliding is adopted in plane coordinate system. The method is considered the geometric characteristics and typical sliding mode of rock - soil mixture slope through continuous change of sliding positions of circle center and calculation effective intersection of arc and line. (2) A calculation and analysis software about rock - soil mixture slope stability is developed by means of C# program for automatic searching combined sliding surfaces and calculating the minimum safety factor in slope section. (3) The research results were ideally applied for landslide improvement design in Lvliang - Linxian railway branch line engineering to improve the design precision and efficiency for many rock - soil mixture slopes，and this method is a good reference for the stability analysis to slope sliding along arc and straight planes.