The full failure,of loading rock samples and concrete samples were tested and its mechanics characteristics and Acoustic Emission (AE) characteristics were studied. The curves of mechanics characteristics and AE accumulative total and AE rate of concrete and rock failure were got. And the AE features including the relationships between AE and time, AE and stress were studied. By comparing the AE characteristics between rock, their different and similar AE characteristics were pointed out. The time-consuming phenomenon was discussed to both rock samples and concrete samples whose plastic deformation is obvious when stress is close to peak value strength at the process of one time loading. It was pointed out that the AE rate of those samples which have this time-consuming phenomenon will be declined and AE quietude will also appear in this stage. But for brittle rocks, neither this time-consuming phenomenon nor AE quietude will appear. In addition, the value of the parameter of time was analyzed and summarized in AE monitoring and studying. Time parameter should be paid more attention to in AE studying despite it could be ignored in general indoor rock mechanics experiment research.