This paper reports the basic problems in aplication of fracture mechanics to concrete. The fracture toughness values obtained by usual toughness test are very higher than that calucurated by surface energy. Glucklich explained this fact by aggreate crack arrest effect. Authors have taken the same view-point and thought that the fracture toughness value of heterogeneous material like concrete is related the energy that is needed to extend macroscopic crack including crack arrest effect. Instead of considering the physical meaning of fracture toughness value furthermore, we have proposed several problems as follows. 1) Dependance of fracture toughness value on crack length 2) Dependance of fracture toughness value on stress field 3) Dependance of fracture toughness value on specimen size effect 4) Dependance of fracture toughness value on artificial flaw geometry 5) Relationship of fracture toughness value to usual non-crack introduced specimen strength As the first step, we have experimented fracture toughness test in tensile splitting and bending. In short crack length, fracture toughness value became very small. So we hypothesized branching crack that is stable crack extension before ultimate failure. Usual non-crack introduced specimen strength is related to fracture toughness and critical crack length. The critical crack length is thought the branching crack of non-crack introduced specimen and depends on aggregates and stress field. As a result of our experiments, we can aply fracture mechanics to concrete. However the fracture toughness value and critical crack length of concrete are very large. This means that concrete is insensitive to crack and it is no merit to aply fracture mechanics method to "macroscopic" failure of concrete.