Since linear fracture mechanics was proposed by Irwin in 1957, its usefulness has been recognized widely. However, there is no detailed discussion about the range of applicability of linear fracture mechanics (Linear Crack Mechanics). Originally, linear fracture mechanics should be called linear crack mechanics. Recently, non-linear crack mechanics was proposed by one of the authors and its usefulness was confirmed though the analysis on the limited numbers of geometrical conditions. Considering these facts, first the effectiveness of non-linear crack mechanics is confirmed by FEM analysis on a wide range of geometrical conditions. Then, the effective range of linear fracture mechanics is discussed based on non-linear crack mechanics, taking as examples the cases of a strip with a center crack and a strip with two edge cracks under tension.