Fully understanding the randomness of rock mechanical parameters and reasonably evaluating its probability distribution are the basis for the objective evaluation of rock engineering stability. About 50 specimens of each kind of igneous rock, i.e. devonite basalt and amygdaloidal basalt gained from the Baihetan Project, are used for uniaxial compression tests respectively. The stochastic distribution characteristics and the optimal probability density function form of characteristic strength, deformation parameter, characteristic strain and fracture surface angle of basalt are studied by means of statistical analysis and hypothesis test. The analysis results show that the discretization is an inherent property of basalt, and only a certain number of repeated tests can reliably assess its basic mechanical properties. The optimal probability distributions of the two kinds of basalt, including the characteristic strength, the deformation parameter, the characteristic strain and the fracture surface angle, are not the same, which are normal distribution, lognormal distribution, Weibull distribution and Weibull distribution. The statistical analysis results can not only enrich our knowledge about rock deformation and failure, but also provide experimental proof for further reliability analysis of geotechnical engineering.