It is important component and also is one of the kernel problem of sustainable development strategy that mineral resources are of sustainable utilization, but the mineral resources are limited, scarce, exhausted and not regenerated resources in the natural world and they are not be of sustainable utilization on theory. Exploited and utilized of them will undoubtedly lead to the result that the ultimate of their reserves is zero. Then，how to define sustainable utilization of minera1 resources has caused the concern of theory circle in recent year．Th．s paper has gone on the quantitative analysis to the replacement problem of exhaustible resources with the math mode1．infers the condition of mineral resources exhaustion an d replacement occurred from economic meaning，and gives a concrete application of the model for instance．It lays a theoretical foundation for further study on fair alloc ation of mineral Reso urces be tween generations，and it has also important practical significa nce for the protection and utilization of mineral resources