The work aims to study the stress-strain variation characteristics of the poplar under the static and dynamic compression loading with the poplar as the research object, and build proper constitutive model to describe it. Through static and dynamic compression loading test on poplar specimen, the stress-strain variation characteristics of the poplar were analyzed, and the constitutive model suitable for the poplar under static and dynamic compression load was built. The study found that under static compression loading of poplar wood from the stress-strain curve was divided into three parts: linear elastic stages, yield stages and densification stage. The dynamic compression loading of poplar wood from the stress-strain curve was divided into two parts: stages of linear elastic and yield. During static compression loading, the axial yield stress of poplar was the largest, and it was 5.70 times and 7.75 times of radial and tangential yield stress respectively. During dynamic compression loading, when the strain rate was increased to 1000 s-1 from 400 s-1, radial, tangential to yield stress and axial was respectively increased by 1.51 times, 1.59 times and 3.12 times; the yield stress of poplar wood had strong strain rate sensitivity. It is more appropriate to describe the constitutive relation under static and dynamic compression loading with constitutive equation containing the influence of strain rate. Poplar is a strain rate sensitive material. Under static and dynamic compression loading, poplar wood from the stress-strain curve shows the characteristics of the porous materials. It is feasible to apply the constitutive model of porous materials to the wood.