The stress-strain curves of polymer bonded explosives (PBXs) are generally nonlinear and poorly unsymmetric.The construction of constitutive model is a difficult problem in the research of mechanical properties of explosives.In this paper, tak-ing PBX-901 as the research object, the uniaxial tension and compression experiments at different temperatures were carried out firstly.Then, a four-parameter and a two-parameter constitutive model were respectively established and the relative undeter-mined parameters were determined based on the Boltzmann function according to S-shaped stress-strain curves obtained.The parameters of two-parameter constitutive model can be determined only using analytical solution including the compression strength and initial segment elastic modulus, and its description error is less than 5%, while the parameters of the four-parameter model though parameter fitting.Finally the second development module of ANSYS software was adopted to realize the numerical application of the two -parameter constitutive model for the Brazilian disk tests.Through comparison with the experimental re-sults, the relative error of numerical results only is about 5.11%.The description precision of the nonlinear two-parameter consti-tutive model established in the text is satisfactory and it meets the needs of engineering