Bamboo is a natural composite material consisting of unidirectional fibre bundles, oriented along axial direction, embedded in soft parenchymatous matrix. The bundles are arranged such that the fibre density (or fibre volume fraction) varies from outer to inner periphery of bamboo shoot. The gradation in volume fraction of unidirectional fibre bundles qualifies bamboo as a typical radially graded transversely isotropic material. Being largely a cellulosic material, the fibre bundles have high tensile strength. However, there is great dispersion of these properties. In this work, an attempt is made to model the progressive failure of fibre bundles to predict the failure strength of bulk bamboo in uniaxial tension. A two-parameter Weibull distribution is proposed to analyse the strengths of fibre bundles having different cross-section areas. Tension tests are performed on fibre bundles, selected from different fibre density regions in the transverse cross-section of bamboo, for determining statistical parameters. The results highlight the close resemblance between the Weibull probability distribution of the experimental results on fibre bundles and overall mechanical behaviour of the bulk bamboo. Thus, the use of Weibull parameters is established for predicting the strength of bulk bamboo from fibre bundle testing of different cross-section areas.