Bamboo scrimber is a unidirectional natural fibrous composite material. It has a broad prospect to be used as a construction material due to its outstanding physical and mechanical properties, especially the mechanical properties along the fibre direction. This study performed the uniaxial longitudinal tensile and compressive tests on bamboo scrimber and presented two stress–strain constitutive models based on the test results. The first one is a two-stage non-linear model, which has a linear function and a quadratic function. The coefficients in this model depend on the material property. The second model is an exponential function on the basis of the elastic–plastic method. The coefficients in this model are obtained by fitting and calibrating the experimental data. The two models are both in good agreement with the experimental results, while the first one is convenient for engineering applications, and the second model can be used to determine the material failure criterion under complex loading at any angle.