The mechanical properties of the structural components (i.e., columns and beams produced from engineered bamboo products), such as, bamboo scrimber (also known as parallel bamboo strand lumber, PBSL) and Laminated Bamboo Lumber (LBL), have attracted considerable attention from researchers in recent years. In previous studies, researchers reported on the stress-strain behaviour of bamboo scrimber, LBL and glue laminated bamboo under compression and proposed some empirical and semi-empirical models, based on their individual studies. However, a generic constitutive model for engineered bamboo products is still not available. The compressive stress-strain curves of bamboo scrimber and LBL are reported to show a similar behaviour with three distinct stages i.e., a linear elastic stage followed by a nonlinear plastic stage and a plateau. As part of the current study, the previously proposed models for bamboo scrimber were carefully studied and all available material test results on engineered bamboo were used to develop a generic constitutive model, based on the Ramberg-Osgood (RO) formulation considering its suitability to capture its material nonlinearity. Based on the test results, it was observed that 1% proof stress can be used in a compound RO model to predict an accurate material response for bamboo scrimber. The proposed modelling technique has also been applied to predict the compressive behaviour of LBL. This paper proposes the RO coefficients for both bamboo scrimber and LBL that can be used to develop accurate nonlinear models for engineered bamboo products.