The avalanche characteristics of destruction of porous dielectric materials are closely related to its failure mechanism. In order to investigate the avalanche characteristics of concrete during tensile and compressive failure based on acoustic emission statistics, the concrete uniaxial compression and Brazil splitting tests were carried out. And the acoustic emission signals in the loading process were monitored, and the statistical characteristics of the acoustic emission signals such as amplitude, absolute energy, duration and waiting time were compared and analyzed. The results show that the maximum acoustic emission energy is distributed near the peak stress, but the number of signals in the splitting process is much lower than that in uniaxial compression. All the b-value increases first and then decreases, and the b-value decreases earlier and the change range is larger under splitting failure, indicating that the large cracks appeared earlier and is more easily destroyed. The probability density distributions of absolute energy, ?amplitude and duration of acoustic emission under tensile and compressive failure conform to the power law, but the corresponding avalanche index values are different, which is related to the failure mechanism during the failure process. The absolute energy distribution of the splitting failure is close to the pure power law distribution, while the compressive failure accords with the damped power law distribution, and the corresponding energy index value is larger. The energy index values of uniaxial compression and Brazilian splitting failure in different time periods show a downward trend, indicating that the proportion of large energy signals in the specimen increase with the increase of load. The probability density distribution of waiting time under tensile and compressive failure is close, which shows the stability, and also shows the applicability of statistical law.