The growth of a crack in a bi-materials base under a building will cause the structure failure. The mechanism of this kind crack growth must be investigated. In this paper, a series of I-II mixed mode crack fracture experiments for bi-materials have been conducted. In some situations, a crack can grow from the weak medium concrete into the hard medium marble under compression load. The stress intensity factors KI ,KII and the first principle stress σ1 near crack tips have been calculated. The difference in crack propagation ability between the single-material and the bi-materials specimens are also studied. The experimental results are in accordance with the σθmax fracture criterion.